ORIGINAL_ARTICLE
A Proximal Point Algorithm for Finding a Common Zero of a Finite Family of Maximal Monotone Operators
In this paper, we consider a proximal point algorithm for finding a common zero of a finite family of maximal monotone operators in real Hilbert spaces. Also, we give a necessary and sufficient condition for the common zero set of finite operators to be nonempty, and by showing that in this case, this iterative sequence converges strongly to the metric projection of some point onto the set of common zeros of operators.
https://scma.maragheh.ac.ir/article_36660_2dd27eb6ca24133e2c7b42b563bb1c1b.pdf
2019-10-01
1
15
10.22130/scma.2019.100821.542
Maximal monotone operator
Proximal point algorithm
Nonexpansive map
Resolvent operator
Mohsen
Tahernia
m.taherniamath@gmail.com
1
Department of Mathematics, Faculty of Science, Arak University, 38156-8-8349, Arak, Iran.
AUTHOR
Sirous
Moradi
sirousmoradi@gmail.com
2
Department of Mathematics, Faculty of Science, Arak University, 38156-8-8349, Arak, Iran.
LEAD_AUTHOR
Somaye
Jafari
s.jafari.math@gmail.com
3
Department of Mathematics, Faculty of Science, Arak University, 38156-8-8349, Arak, Iran.
AUTHOR
[1] H.H. Bauschke, P.L. Combettes, and S. Reich, The asymptotic behavior of the composition of two resolvents, Nonlinear Anal. (TMA), 60 (2005), pp. 283-301.
1
[2] H.H. Bauschke, E. Matouskova, and S. Reich, Projection and proximal point methods: convergence results and counterexamples, Nonlinear Anal. (TMA), 56 (2004), pp. 715-738.
2
[3] O.A. Boikanyo and G. Morosanu, A contraction proximal point algorithm with two monotone operators, Nonlinear Anal. (TMA), 75 (2012), pp. 5686-5692.
3
[4] O.A. Boikanyo and G. Morosanu, On the method of alternating resolvents, Nonlinear Anal. (TMA), 74 (2011), pp. 5147-5160.
4
[5] O.A. Boikanyo and G. Morosanu, Strong convergence of the method of alternating resolvents, J. Nonlinear Convex Anal., 14 (2013), pp. 221-229.
5
[6] O.A. Boikanyo and G. Morosanu, The method of alternating resolvents revisited, Numer. Funct. Anal. Optim., 33 (2012), pp. 1280-1287.
6
[7] L.M. Bregman, The method of successive projection for finding a common point of convex sets, Sov. Math. Dokl., 6 (1965), pp. 688-692.
7
[8] K. Goebel and S. Reich, Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings, Marcel Dekker, New York and Basel, 1984.
8
[9] H. Hundal, An alternating projection that does not converge in norm, Nonlinear Anal. (TMA), 57 (2004), pp. 35-61.
9
[10] E. Kopecka and S. Reich, A note on the von Neumann alternating projections algorithm, J. Nonlinear Convex Anal., 5 (2004), pp. 379-386.
10
[11] P.E. Mainge, Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization, Set-Valued Anal., 16 (2008), pp. 899-912.
11
[12] E. Matouskova and S. Reich, The Hundal example revisited, J. Nonlinear Convex Anal., 4 (2003), pp. 411-427.
12
[13] G. Morosanu, Nonlinear Evolution Equations and Applications, Reidel, Dordrecht, 1988.
13
[14] L. Nasiri and A. Sameripour, The spectral properties of differential operators with matrix coefficients on elliptic systems with boundary conditions, Sahand Commun. Math. Anal., 10 (2018), pp. 37-46.
14
[15] N. Nimit, A.P. Farajzadeh, and N. Petrot, Adaptive subgradient method for the split quasi-convex feasibility problems, Optimization, 65 (2016), pp. 1885-1898.
15
[16] H.K. Xu, A regularization method for the proximal point algorithm, J. Glob. Optim., 36 (2006), pp. 115-125.
16
[17] P. Yatakoat, A new approximation method for common fixed points of a finite family of nonexpansive non-self mappings in Banach spaces, Int. J. Nonlinear Anal. Appl., 9 (2018), pp. 223-234.
17
ORIGINAL_ARTICLE
Diameter Approximate Best Proximity Pair in Fuzzy Normed Spaces
The main purpose of this paper is to study the approximate best proximity pair of cyclic maps and their diameter in fuzzy normed spaces defined by Bag and Samanta. First, approximate best point proximity points on fuzzy normed linear spaces are defined and four general lemmas are given regarding approximate fixed point and approximate best proximity pair of cyclic maps on fuzzy normed spaces. Using these results, we prove theorems for various types of well-known generalized contractions in fuzzy normed spaces. Also, we apply our results to get an application of approximate fixed point and approximate best proximity pair theorem of their diameter.
https://scma.maragheh.ac.ir/article_36659_89544cc8cecc2b2c61d92c42dffa6116.pdf
2019-10-01
17
34
10.22130/scma.2018.83850.420
Cyclic maps
$alpha$-asymptotically regular
$F$-Kannan operator
Fuzzy diameter
Seyed Ali Mohammad
Mohsenialhosseini
mohsenhosseini@yazd.ac.ir
1
Faculty of Mathematics, Yazd University, Yazd, Iran and Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.
AUTHOR
Morteza
Saheli
saheli@vru.ac.ir
2
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.
LEAD_AUTHOR
[1] T. Bag and S.K. Samanta, Finite dimensional fuzzy normed linear spaces, J. Fuzzy Math., 11 (2003), pp. 687-705.
1
[2] T. Bag and S.K. Samanta, Fuzzy bounded linear operators, Fuzzy Sets and Systems, 151 (2005), pp. 513-547.
2
[3] T. Bag and S.K. Samanta, Some fixed point theorems in fuzzy normed linear spaces, Inf. Sci., 177 (2007), pp. 3271-3289.
3
[4] M. Berinde, Approximate fixed point theorems, Mathematica, LI (1) (2006).
4
[5] V. Berinde, Approximating fixed points of weak contractions using the Picard iteration, Nonlinear Anal. Forum, 9 (2004).
5
[6] V. Berinde, On the approximation of fixed points of weak contractive mappings, Math., 19 (2003), pp. 7-22.
6
[7] S.K. Chatterjea, Fixed-point theorems, C.R. Acad. Bulgare Sci. 25 (1972), pp. 727-730.
7
[8] S.C. Cheng and J.N. Mordeson, Fuzzy linear operator and fuzzy normed linear spaces, Bull. Calcutta Math. Soc., 86 (1994), pp. 429-436.
8
[9] A. Chitra and P.Y. Mordeson, Fuzzy linear operators and fuzzy normed linear spaces, Bull. Calcutta Math. Soc., 74 (1969), pp. 660-665.
9
[10] Lj. B. Ciric, A generalization of Banach’s contraction principle, Proc. Am. Math. Soc., 45 (1974), pp. 267-273.
10
[11] C. Felbin, Finite dimensional fuzzy normeded linear spaces, Fuzzy Sets and Systems, 48 (1992), pp. 239-248.
11
[12] O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy Sets and Systems, 12 (1984), pp. 215-229.
12
[13] R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc., 10 (1968), pp. 71-76.
13
[14] A.K. Katsaras, Fuzzy topological vector spaces II, Fuzzy Sets and Systems, 12 (1984), pp. 143-154.
14
[15] I. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica, 11 (1975), pp. 326-334.
15
[16] S.A.M. Mohsenalhosseini, Approximate fixed point theorems in fuzzy norm spaces for an operator, Advances in Fuzzy Systems, 2013, Article ID 613604, 8 pages.
16
[17] S.A.M. Mohsenalhosseini, Approximate best proximity pairs in metric space for Contraction Maps, Advances in Fixed Point Theory, 4 (2014), pp. 310-324.
17
[18] S.A.M. Mohsenalhosseini, H. Mazaheri, and M.A. Dehghan, Approximate best proximity pairs in metric space, Abstract and Applied Analysis, (2011), Article ID 596971, 9 pages.
18
[19] S.A.M. Mohsenalhosseini, H. Mazaheri, and M.A. Dehghan, Approximate fixed point in fuzzy normed spaces for nonlinear maps, Iranin Journal of Fuzzy Systems, 10 (2013), pp. 135-142.
19
ORIGINAL_ARTICLE
Fixed Point Theory in $\varepsilon$-connected Orthogonal Metric Space
The existence of fixed point in orthogonal metric spaces has been initiated by Eshaghi and et. al [7]. In this paper, we prove existence and uniqueness theorem of fixed point for mappings on $\varepsilon$-connected orthogonal metric space. As a consequence of this, we obtain the existence and uniqueness of fixed point for analytic function of one complex variable. The paper concludes with some illustrating examples.
https://scma.maragheh.ac.ir/article_36366_988f1f54affa1680ce562c8d50a002e5.pdf
2019-10-01
35
46
10.22130/scma.2018.72368.289
Fixed point
$varepsilon$-connected
Orthogonal set
solution
Metric space
Analytic function
Madjid
Eshaghi Gordji
meshaghi@semnan.ac.ir
1
Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran.
AUTHOR
Hasti
Habibi
hastihabibi1363@gmail.com
2
Department of Mathematics, Semnan University, Semnan, Iran.
LEAD_AUTHOR
[1] H. Baghani, M. Eshaghi Gordji, and M. Ramezani, Orthogonal sets: their relation to the axiom of choice and a generalized fixed point theorem, J. Fixed Point Theory Appl., 18 (2016), pp. 465-477.
1
[2] I. Beg and A.R. Butt, Fixed point of set-valued graph contractive mappings, J. Inequa. Appl., (2013), 2013:252.
2
[3] M. Edelstein, An extension of Banach's contraction principle, Proc. Amer. Math. Soc., 12 (1961), pp. 7-10.
3
[4] M. Eshaghi Gordji, H. Baghani, H. Khodaei, and M. Ramezani, A generalization of Nadler's fixed point theorem, J. Nonlinear Sci. Appl., 3 (2010), pp. 148-151.
4
[5] M. Eshaghi Gordji, H. Baghani, H. Khodaei, and M. Ramezani, Generalized multi valued contraction mappings, J. Comput. Anal. Appl., 13 (2011), pp. 730-733.
5
[6] M. Eshaghi Gordji, H. Baghani, H. Khodaei, and M. Ramezani, Geraghty's fixed point theorem for special multi-valued mappings, Thai. J. Math., 10 (2012), pp. 225-231.
6
[7] M. Eshaghi Gordji, M. Ramezani, M. De La Sen, and Y.J. Cho, On orthogonal sets and Banach fixed point theorem, Fixed Point Theory, 18 (2017), pp. 569-578.
7
[8] R. Espinola, E.S. Kim, and W.A. Kirk, Fixed point properties of mappings satisfying local contractive conditions, Nonlinear Anal. Forum, 6 (2001), pp. 103-111.
8
[9] N. Mehmood, A. Azam, and S. Aleksic, Topological vector-space valued cone Banach spaces, Int. J. Anal. Appl., 6 (2014), pp. 205-219.
9
[10] M. Ramezani, Orthogonal metric space and convex contractions, Int. J. Nonlinear Anal. Appl., 6 (2015), pp. 127-132.
10
[11] M. Ramezani, H. Baghani, Contractive gauge functions in strongly orthogonal metric spaces, Int. J. Nonlinear Anal. Appl., 8 (2017), pp. 23-28.
11
[12] P. Shahi, J. Kaur, and S.S. Bhatia, On fixed points of generalized $alpha$-$phi$ contractive type mappings in partial metric spaces, Int. J. Anal. Appl., 12 (2016), pp. 38-48.
12
ORIGINAL_ARTICLE
$p$-adic Dual Shearlet Frames
We introduced the continuous and discrete $p$-adic shearlet systems. We restrict ourselves to a brief description of the $p$-adic theory and shearlets in real case. Using the group $G_p$ consist of all $p$-adic numbers that all of its elements have a square root, we defined the continuous $p$-adic shearlet system associated with $L^2\left(Q_p^{2}\right)$. The discrete $p$-adic shearlet frames for $L^2\left(Q_p^{2}\right)$ is discussed. Also we prove that the frame operator $S$ associated with the group $G_p$ of all with the shearlet frame $SH\left( \psi; \Lambda\right)$ is a Fourier multiplier with a function in terms of $\widehat{\psi}$. For a measurable subset $H \subset Q_p^{2}$, we considered a subspace $L^2\left(H\right)^{\vee}$ of $L^2\left(Q_p^{2}\right)$. Finally we give a necessary condition for two functions in $L^2\left(Q_p^{2}\right)$ to generate a p-adic dual shearlet tight frame via admissibility.
https://scma.maragheh.ac.ir/article_34965_b1db50eb43891d7297fa1e8dc1a5b630.pdf
2019-10-01
47
56
10.22130/scma.2018.77684.355
$p$-adic numbers
Dual frame
$p$-adic shearlet system
$p$-adic dual tight frame
Mahdieh
Fatemidokht
fatemidokht@gmail.com
1
Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
AUTHOR
Ataollah
Askari Hemmat
askari@uk.ac.ir
2
Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
LEAD_AUTHOR
[1] O. Christensen, An introduction to Frames and Riesz Bases, Birkhauser, Boston, 2003.
1
[2] S. Dahlke, G. Kutyniok, P. Maass, C. Sagiv, H.-G. Stark, and G. Teschke, The uncertainty principle associate with the continuous shearlet transform, Int. J. Wavelets Multiresolute. Inf. Process., 6 (2008), pp. 157-181.
2
[3] M. Fatemidokht and A. Askari Hemmat, $P$-adic shearlets, Wavel. Linear Algebra, to appear
3
[4] B. Han, On dual wavelet tight frames, Appl. Comput. Harmon. Anal., 4 (1997), pp. 380-413.
4
[5] G. Kutyniok and D. Labate, Construction of regular and irregular shearlet frames, J. Wavelet Theory Appl., 1 (2007), pp. 1-10.
5
[6] G. Kutyniok and D. Labate, Shearlets: Multiscle Analysis for Multivariate Data, Birkhauser. Basel, 2012.
6
[7] V.S. Valdimirov, I.V. Volovich, and E.I. Zelenov, $p$-Adic Analysis and Mathematical Physics, World Scientific, Singapore, 1994.
7
ORIGINAL_ARTICLE
Simple Construction of a Frame which is $\epsilon$-nearly Parseval and $\epsilon$-nearly Unit Norm
In this paper, we will provide a simple method for starting with a given finite frame for an $n$-dimensional Hilbert space $\mathcal{H}_n$ with nonzero elements and producing a frame which is $\epsilon$-nearly Parseval and $\epsilon$-nearly unit norm. Also, the concept of the $\epsilon$-nearly equal frame operators for two given frames is presented. Moreover, we characterize all bounded invertible operators $T$ on the finite or infinite dimensional Hilbert space $\mathcal{H}$ such that $\left\{f_k\right\}_{k=1}^\infty$ and $\left\{Tf_k\right\}_{k=1}^\infty$ are $\epsilon$-nearly equal frame operators, where $\left\{f_k\right\}_{k=1}^\infty$ is a frame for $\mathcal{H}$. Finally, we introduce and characterize all operator dual Parseval frames of a given Parseval frame.
https://scma.maragheh.ac.ir/article_36056_f35fed1254b0f7e914d2501ed969db8f.pdf
2019-10-01
57
67
10.22130/scma.2018.79613.374
Frame
Parseval frame
$epsilon$-nearly Parseval frame
$epsilon$-nearly equal frame operators
Operator dual Parseval frames
Mohammad Ali
Hasankhani Fard
m.hasankhani@vru.ac.ir
1
Department of Mathematics Vali-e-Asr University, Rafsanjan, Iran.
LEAD_AUTHOR
[1] P. Balazs, J.P. Antoine, and A. Grybos, Weighted and Controlled Frames: Mutual Relationship and first Numerical Properties, Int. J. Wavelets Multiresolut. Inf. Process., 109 (2010), pp. 109-132.
1
[2] J.J. Benedetto, Frame Decomposition, Sampling, and Uncertainty Principle Inequalities in "Wavelets: Mathematics and Applications" (J.J. Benedetto and M.W. Frazier, Eds.), CRC Press., Boca Raton, FL, 1994.
2
[3] B.G. Bodmann and P.G. Casazza, The road to equal-norm Parseval frames, J. Funct. Anal., 258 (2010), pp. 397-420.
3
[4] J. Cahill, P.G. Casazza, and G. Kutyniok, Operators and frames, J. Operator Theory., 70 (2013), pp. 145-164.
4
[5] P.G. Casazza and J. Kovacevic, Equal-norm tight frames with erasures, Adv. Comput. Math., 18 (2003), pp. 387-430.
5
[6] O. Christensen, An Introduction to Frames and Riesz Bases, Birkhauser., Boston, Basel, Berlin, 2002.
6
[7] O. Christensen and Y. Eldar, Oblique dual frames and shift-invariant spaces, Appl. Comput. Harmon. Anal., 17 (2004), pp. 48-68.
7
[8] O. Christensen and R.S. Laugesen, Approximately dual frames in Hilbert spaces and application to Gabor frames, Sampl. Theory Signal Image Process., 9 (2011), pp. 77-90.
8
[9] D. Freeman and D. Speegle, The discretization problem for continuous frames., https://arxiv.org/abs/1611.06469.
9
[10] V.K. Goyal, J. Kovacevic, and J.A. Kelner, Quantized frame expansions with erasures, Appl. Comput. Harmon. Anal., 10 (2001), pp. 203-233.
10
[11] C. Heil, Y.Y. Koo, and J.K. Lim, Duals of frame sequences, Acta Appl. Math., 107 (2008), pp. 75-90.
11
[12] C. Heil and D. Walnut, Continuous and discrete wavelet transform, SIAM Rev., 31 (1969), pp. 628-666.
12
[13] A.A. Hemmat and J.P. Gabardo, Properties of oblique dual frames in shift-invariant systems, J. Math. Anal. Appl., 356 (2009), pp. 346-354.
13
[14] S. Li and H. Ogawa, Pseudo duals of frames with applications, Appl. Comput. Harmon. Anal., 11 (2001), pp. 289-304.
14
[15] R. Young, An Introduction to Nonharmonic Fourier Series, Academic Press., New York, 1980.
15
ORIGINAL_ARTICLE
Coefficient Estimates for Some Subclasses of Analytic and Bi-Univalent Functions Associated with Conic Domain
The main objective of this investigation is to introduce certain new subclasses of the class $\Sigma $ of bi-univalent functions by using concept of conic domain. Furthermore, we find non-sharp estimates on the first two Taylor-Maclaurin coefficients $ \left \vert a_{2}\right \vert $ and $\left \vert a_{3}\right \vert $ for functions in these new subclasses. We consider various corollaries and consequences of our main results. We also point out relevant connections to some of the earlier known developments.
https://scma.maragheh.ac.ir/article_36057_c5109d49de17a43b53100e7a3a2631d1.pdf
2019-10-01
69
81
10.22130/scma.2018.87581.449
Univalent function
Analytic function
Bi-univalent function
Subordination between analytic functions
Starlike and strongly starlike functions
Conic domain
Muhamamd
Tahir
tahirmuhammad778@gmail.com
1
Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan.
AUTHOR
Nazar
Khan
nazarmaths@gmail.com
2
Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan.
AUTHOR
Qazi Zahoor
Ahmad
zahoorqazi5@gmail.com
3
Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan.
AUTHOR
Bilal
Khan
bilalmaths789@gmail.com
4
Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan.
LEAD_AUTHOR
Gul Mehtab
Khan
mehtabmaths789@gmail.com
5
Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan.
AUTHOR
[1] N.I. Ahiezer, Elements of theory of elliptic functions, Moscow, 1970.
1
[2] G.D. Anderson, M.K. Vamanamurthy, and M.K. Vourinen, Conformal invariants, inequalities and quasiconformal maps, Wiley-Interscience, 1997.
2
[3] M. Arif, J. Dziok, M. Raza, and J. Sokol, On products of multivalent close-to-star functions, J. Ineq. appl., 2015 (2015), pp. 1-14.
3
[4] S.Z.H. Bukhari, M. Nazir, and M. Raza, Some generalisations of analytic functions with respect to 2k-symmetric conjugate points, Maejo Int. J. Sci. Technol., 2016, pp. 10, 1-12.
4
[5] P.L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften (Fundamental Principles of Mathematical Science), vol. 259, Springer-Verlag, New York, Berlin, 1983.
5
[6] B.A. Frasin, Coefficient bounds for certain classes of bi-univalent functions, Hacettepe J. Math. Stat., 43 (2014), pp. 383-389.
6
[7] S. Hussain, N. Khan, S. Khan, and Q.Z. Ahmad, On a subclass of analytic and bi-univalent functions, Southeast Asian Bull. Math., article in press.
7
[8] S. Kanas and A. Wisniowska, Conic regions and k-uniform convexity, J. Comput. Appl. Math., 105 (1999), pp. 327-336.
8
[9] S. Kanas and A. Wisniowska, Conic domains and starlike functions, Rev. Roumaine Math. Pures Appl., 45 (2000), pp. 647-657.
9
[10] S. Kanas, Coefficient estimates in subclasses of the Caratheodory class related to conical domains, Acta Math. Univ. Comenian., 74 (2005), pp. 149-161.
10
[11] N. Khan, B. Khan, Q.Z. Ahmad, and S. Ahmad, Some Convolution Properties of Multivalent Analytic Functions, AIMS Math., 2 (2017), pp. 260-268.
11
[12] N. Khan, Q.Z. Ahmad, T. Khalid, and B. Khan, Results on spirallike $p$-valent functions, AIMS Math., 3 (2018), pp. 12-20.
12
[13] N. Khan, A. Khan, Q.Z. Ahmad, B. Khan, and S. Khan, Study of multivalent spirallike Bazilevic functions AIMS Math., 3 (2018), pp. 353-364.
13
[14] K.I. Noor, N. Khan, M. Darus, Q.Z. Ahmad, and B. Khan, Some properties of analytic functions associated with conic type regions, Intern. J. Anal. Appl., 16 (2018), pp. 689-701.
14
[15] K.I. Noor, On a generalization of uniformly convex and related functions, Comput. Math. Appl., 61 (2011), pp. 117-125.
15
[16] K.I. Noor, M. Arif, and M.W. Ul-Haq, On $k$-uniformly close-to-convex functions of complex order, Appl. Math. Comput., 215 (2009), pp. 629-635.
16
[17] K.I. Noor, Q.Z. Ahmad, and M.A. Noor, On some subclasses of analytic functions defined by fractional derivative in the conic regions, Appl. Math. Inf., Sci., 9 (2015), pp. 8-19.
17
[18] K.I. Noor, J. Sokol, and Q.Z. Ahmad, Applications of conic type regions to subclasses of meromorphic univalent functions with respect to symmetric points, RACSAM, 2016, pp. 1-14.
18
[19] K.I. Noor, Q.Z. Ahmad, and N. Khan, On some subclasses of meromorphic functions defined by fractional derivative operator, Italian J. Pure. App Math., (2017), pp. 1-8.
19
[20] K.I. Noor and N. Khan, Some convolution properties of a subclass of p-valent functions, Maejo Int. J. Sci. Technol., 9 (2015), pp. 181-192.
20
[21] M. Nunokawa, S. Hussain, N. Khan, and Q.Z. Ahmad, A subclass of analytic functions related with conic domain, J. Clas. Anal., 9 (2016), pp. 137-149.
21
[22] M. Obradovic and S. Owa, Some sufficient conditions for strongly starlikeness, Int. J. Math. Math. Sci., 24 (2000), pp. 643-647.
22
[23] M. Raza, M. U Din, and S.N. Malik, Certain geometric properties of normalized wright functions, J. Func. Spaces, 2016 (2016), 9 pages.
23
[24] W. Rogosinski, On the coefficients of subordinate functions, Proc. Lond. Math. Soc., 48 (1943), pp. 48-82.
24
[25] H.M. Srivastava, A.K. Mishra, and P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., 23 (2010), pp. 1188-1192.
25
[26] H.M. Srivastava, S. Bulut, M. Caglar, and N. Yagmur, Coefficient estimates for a general subclass of analytic and bi-univalent functions, Filomat, 27 (2013), pp. 831-842.
26
[27] H.M. Srivastava, and D. Bansal, Coefficient estimates for a subclass of analytic and bi-univalent functions, J. Egyptian Math. Soc., 23 (2015), pp. 242-246.
27
[28] H.M. Srivastava, G. Murugusundaramoorthy, and N. Magesh, Certain subclasses of bi-univalent functions associated with the Hohlov operator, Global J. Math. Anal., 1 (2013), pp. 67-73.
28
[29] W.Ul-Haq and S. Manzar, Coefficient Estimates for Certain Subfamilies of Close-to-Convex Functions of Complex Order, Filomat, 30 (2016), pp. 99-103.
29
[30] W. Ul-Haq, A. Nazneen, and N. Rehman, Coefficient estimates for certain subfamilies of close-to-convex functions of complex order, Filomat, 28 (2014), pp. 1139-1142.
30
[31] W. Ul-Haq, A. Nazneen, M. Arif, and N. Rehman, Coefficient estimate of certain subfamily of close to convex functions, J. Comput. Anal. Appl., 16 (2013), pp. 133-138.
31
[32] W. Ul-Haq and S. Mahmmod, Certain properties of a subfamily of close-to-convex functions related to conic regions, Abst. Appl. Anal., Article ID: 847287, 2013 (2013), 6 pp.
32
[33] Q.-H. Xu, H.-G. Xiao, and H. M. Srivastava, A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems, Appl. Math. Comput., 218 (2012),
33
ORIGINAL_ARTICLE
$L_{p;r} $ spaces: Cauchy Singular Integral, Hardy Classes and Riemann-Hilbert Problem in this Framework
In the present work the space $L_{p;r} $ which is continuously embedded into $L_{p} $ is introduced. The corresponding Hardy spaces of analytic functions are defined as well. Some properties of the functions from these spaces are studied. The analogs of some results in the classical theory of Hardy spaces are proved for the new spaces. It is shown that the Cauchy singular integral operator is bounded in $L_{p;r} $. The problem of basisness of the system $\left\{A\left(t\right)e^{{\mathop{\rm int}} }; B\left(t\right)e^{-{\mathop{\rm int}} } \right\}_{n\in Z_{+} }, $ is also considered. It is shown that under an additional condition this system forms a basis in $L_{p;r} $ if and only if the Riemann-Hilbert problem has a unique solution in corresponding Hardy class ${ H}_{p;r}^{+} \times { H}_{p;r}^{+} $.
https://scma.maragheh.ac.ir/article_36058_e30acb2ad0eafa93148679627a197562.pdf
2019-10-01
83
91
10.22130/scma.2018.81285.391
Function space
Hardy class
singular integral
Riemann-Hilbert problem
Ali
Huseynli
alihuseynli@gmail.com
1
Department of Mathematics, Khazar University, AZ1096, Baku, Azerbaijan and Department of Non-harmonic analysis, Institute of Mathematics and Mechanics of NAS of Azerbaijan, AZ1141, Baku, Azerbaijan.
LEAD_AUTHOR
Asmar
Mirzabalayeva
esmer26@mail.ru
2
Department of Non-harmonic analysis", Institute of Mathematics and Mechanics of NAS of Azerbaijan, AZ1141, Baku, Azerbaijan.
AUTHOR
[1] D.R. Adams, Morrey spaces, Springer, 2016.
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[4] B.T. Bilalov and Z.G. Guseynov, Basicity of a system of exponents with a piece-wise linear phase in variable spaces, Mediterr. J. Math., 9 (2012), pp. 487-498.
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[6] B.T. Bilalov and A.A. Quliyeva, On basicity of exponential systems in Morrey-type spaces, Internat. J. Math., 25 (2014), 10 pages.
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[8] J.B. Conway, Functions of one complex variable, II, Springer-Verlag, 2012.
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[9] D.V. Cruz-Uribe and A. Fiorenza, Variable Lebesgue spaces: Foundations and Harmonic Analysis, Springer, 2013.
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[10] L. Diening, P. Harjulehto, P. Hasto, and M. Ruzicka, Lebesgue and Sobolev spaces with variable exponents, Springer-Verlag, Berlin, 2017.
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[11] G.M. Goluzin, Geometric theory of functions of complex variables, AMS Trans. Math. Monographes, 29, 1969.
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[12] D.M. Israfilov and N.P. Tozman, Approximation in Morrey--Smirnov classes, Azerb. J. Math., 1 (2011), pp. 99-113.
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[13] Y. Katznelson, Sets of uniqueness for some classes of trigonometric series, Bull. Amer. Math. Soc., 70 (1964), 722-723.
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[14] V. Kokilashvili, A. Meskhi, H. Rafeiro, and S. Samko, Integral Operators in Non-standard function spaces, Birkhauser, 2, 2016.
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[15] P. Koosis, Introduction to $H_p$ spaces, 2nd edition, CUP, 1998.
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[16] S.M. Nikolski, Approximation of functions of several variables and embedding theorems, Nauka, Moscow, 1969.
16
ORIGINAL_ARTICLE
Generalized $F$-contractions in Partially Ordered Metric Spaces
We discuss about the generalized $F$-contraction mappings in partially ordered metric spaces. For this, we first introduce the notion of ordered weakly $F$-contraction mapping. We also present some fixed point results about this type of mapping in partially ordered metric spaces. Next, we introduce the notion of $\acute{\mathrm{C}}$iri$\acute{\mathrm{c}}$ type generalized ordered weakly $F$-contraction mapping. We also prove some fixed point results about this notion in partially ordered metric spaces. We also provide an example to support our results. In fact, this example shows that our main theorem is a genuine generalization in the area of the generalized $F$-contraction mappings in partially ordered metric spaces.
https://scma.maragheh.ac.ir/article_36059_bd5685c96b785d3676909c2ba3cf34a2.pdf
2019-10-01
93
104
10.22130/scma.2018.81871.398
Fixed point
$F$-contraction
Ordered weakly $F$-contraction
Generalized $F$-contraction
$acute{mathrm{C}}$iri$acute{mathrm{c}}$ type mappings
Seyede Samira
Razavi
srazavi@mail.kntu.ac.ir
1
Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran.
AUTHOR
Hashem
Parvaneh Masiha
masiha@kntu.ac.ir
2
Faculty of Mathematics, K. N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran.
LEAD_AUTHOR
[1] M. Abbas, T. Nazir, and S. Radenovic, Common fixed points of four maps in partially ordered metric spaces, Appl. Math. Lett., 24 (2011), pp. 1520-1526.
1
[2] O. Acar, G. Durmaz, and G. Minak, Generalized multivalued F-contractions on complete metric spaces, Bull. Iranian Math. Soc., 40 (2014), pp. 1469-1478.
2
[3] R.P. Agarwal, M.A. El-Gebeily, and D. O’Regan, Generalized contractions in partially ordered metric spaces, Appl. Anal., 87 (2008), pp. 109-116.
3
[4] S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fund. Math., 3 (1922), pp. 133-181.
4
[5] Lj.B. Ciric, A generalization of Banach’s contraction principle, Proc. Amer. Math. Soc., 45 (1974), pp. 267-273.
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[6] Lj.B. Ciric, M. Abbas, R. Saadati, and N. Hussain, Common fixed points of almost generalized contractive mappings in ordered metric spaces, Appl. Math. Comput., 217 (2011), pp. 5784-5789.
6
[7] W.S. Du, Some new results and generalizations in metric fixed point theory, Nonlinear Anal., 73 (2010), pp. 1439-1446.
7
[8] G. Durmaz, G. Mınak, and I. Altun, Fixed points of ordered F-contractions, Hacet. J. Math. Stat., 45 (2016), pp. 15-21.
8
[9] P. Kumam, F. Rouzkard, M. Imdad, and D. Gopal, Fixed point theorems on ordered metric spaces through a rational contraction, Abstr. Appl. Anal., (2013), Article ID 206515, 9 pages.
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[10] J. Matkowski, Fixed point theorems for mappings with a contractive iterate at a point, Proc. Amer. Math. Soc., 62 (1977), pp. 344-348.
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[11] G. Minak, A. Helvasi, and I. Altun, Ciric type generalized $F$-contractions on complete metric spaces and fixed point results, Filomat., 28 (2014), No. 6, pp. 1143-1151
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[12] H.K. Nashine and I. Altun, A common fixed point theorem on ordered metric spaces, Bull. Iranian Math. Soc., 38 (2012), pp. 925-934.
12
[13] J.J. Nieto and R.R. Lopez, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equation, Order., 22 (2005), pp. 223-239.
13
[14] J.J. Nieto and R.R. Lopez, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sinica (English Ser.), 23 (2007), pp. 2205-2212.
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[15] D. O’Regan and A. Petrusel, Fixed point theorems for generalized contractions in ordered metric spaces, J. Math. Anal. Appl., 341 (2008), pp. 1241-1252.
15
[16] A.C.M. Ran and M.C.B. Reurings, A fixed point theorem in partially ordered sets and some application to matrix equations, Proc. Amer. Math. Soc., 132 (2004), pp. 1435-1443.
16
[17] B.E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal., 47 (2001), pp. 2683-2693.
17
[18] A. Tarski, A lattice-theoretical fixpoint theorem and its applications, Pacific J. Math., 5 (1955), pp. 285-309., MR0074376.
18
[19] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 94 (2012), 6 pages.
19
ORIGINAL_ARTICLE
Some Properties of $ \ast $-frames in Hilbert Modules Over Pro-C*-algebras
In this paper, by using the sequence of adjointable operators from pro-C*-algebra $ \mathcal{A} $ into a Hilbert $ \mathcal{A} $-module $ E $. We introduce frames with bounds in pro-C*-algebra $ \mathcal{A} $. New frames in Hilbert modules over pro-C*-algebras are called standard $ \ast $-frames of multipliers. Meanwhile, we study several useful properties of standard $ \ast $-frames in Hilbert modules over pro-C*-algebras and investigate conditions that under which the sequence ${ \{ {h_i} \}_{i \in I} }$ is a standard $ \ast $-frame of multipliers for Hilbert modules over pro-C*-algebras. Also the effect of operators on standard $ \ast $-frames of multipliers for $ E $ is examined. Finally, compositions of standard $ \ast $-frames in Hilbert modules over pro-C*-algebras are studied.
https://scma.maragheh.ac.ir/article_36278_bf43f599dbf871d99cf80e3655101b74.pdf
2019-10-01
105
117
10.22130/scma.2018.75253.328
Hilbert modules over pro-C*-algebras
Standard $ ast $-frame of multipliers
$ ast $-frame operator
Pre-$ ast $-frame
Mona
Naroei Irani
m.naroei.math@gmail.com
1
Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran.
AUTHOR
Akbar
Nazari
nazari@uk.ac.ir
2
Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
LEAD_AUTHOR
[1] M. Azhini and N. Haddadzadeh, Fusion frames in Hilbert modules over pro-C*-algebras, Int. J. Industrial Math., 5 (2013), pp. 109-118.
1
[2] P.G. Casazza and G. Kutyniok, Frames of subspaces, Contemp. Math., Amer. Math. Soc., 345 (2004), pp. 87-113.
2
[3] I. Daubechies, A. Grossmann, and Y. Meyer, Painless nonorthogonal expansions, J. Math. Phys., 27 (1986), pp. 1271-1283.
3
[4] R.J. Duffin and A.C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc., 72 (1952), pp. 341-366.
4
[5] M. Frank and D.R. Larson, Frames in Hilbert C*-modules and C*-algebras, J. Operator Theory., 48 (2002), pp. 273-314.
5
[6] N. Haddadzadeh, G-frames in Hilbert pro-C*-modules, Int. Electron. J. Pure Appl. Math., 105 (2015), pp. 727-743.
6
[7] M. Joita, Hilbert Modules Over Locally C*-Algebras, University of Bucharest Press, ISBN 973737128-3, 2006.
7
[8] M. Joita, On frames in Hilbert modules over pro-C*-algebras, Topology and its Applications., 156 (2008), pp. 83-92.
8
[9] A. Khosravi and B. Khosravi, Fusion frames and g-frames in Hilbert C*-modules, Int. J. Wavelets Multiresolution. Inf., 6 (2008), pp. 433-466.
9
[10] W.L. Paschke, Inner product modules over B*-algebras, Trans. Amer. Math. Soc., 182 (1973), pp. 443-468.
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[11] I. Raeburn and S.J. Thompson, Countably generated Hilbert modules, the Kasparov stabilisation theorem, and frames with Hilbert modules, Proc. Amer. Math. Soc., 131 (2003), pp. 1557-1564.
11
[12] W. Sun, G-frames and g-Riesz bases, J. Math. Anal. Appl., 322 (2006), pp. 437-452.
12
ORIGINAL_ARTICLE
Some Results about the Contractions and the Pendant Pairs of a Submodular System
Submodularity is an important property of set functions with deep theoretical results and various applications. Submodular systems appear in many applicable area, for example machine learning, economics, computer vision, social science, game theory and combinatorial optimization. Nowadays submodular functions optimization has been attracted by many researchers. Pendant pairs of a symmetric submodular system play essential role in finding a minimizer of this system. In this paper, we investigate some relations between pendant pairs of a submodular system and pendant pairs of its contractions. For a symmetric submodular system $\left(V,f\right)$ we construct a suitable sequence of $\left|V\right|-1$ pendant pairs of its contractions. By using this sequence, we present some properties of the system and its contractions. Finally, we prove some results about the minimizers of a posimodular function.
https://scma.maragheh.ac.ir/article_36279_8d135d8fd6e9c532ae60aff53488a3d6.pdf
2019-10-01
119
128
10.22130/scma.2018.91924.481
Submodular system
Submodular optimization
Maximum adjacency ordering
Posimodular functions
Pendant pairs
st-cut
Saeid
Hanifehnezhad
saeid.hanifehnezhad@gmail.com
1
Department of Mathematics, Shahed University, Tehran, Iran.
AUTHOR
Ardeshir
Dolati
dolati@shahed.ac.ir
2
Department of Computer Science, Shahed University, Tehran, Iran.
LEAD_AUTHOR
[1] D. Dadush, L.A. V'egh, and G. Zambelli, Geometric rescaling algorithms for submodular function minimization, in: Proc. 29th Annual ACM-SIAM Symposium on Discrete Algorithms, New Orleans, Louisiana, USA, 2018, 832-848.
1
[2] S. Fujishige, Submodular functions and optimization, Elsevier., Amesterdam, 2005.
2
[3] M.X. Goemans and J.A. Soto, Algorithms for symmetric submodular function minimization under hereditary constraints and generalizations, SIAM J. Discrete Math., 27 (2013), pp. 1123-1145.
3
[4] M. Gr"otschel, L. Lov'asz, and A. Schrijver, The ellipsoid method and its consequences in combinatorial optimization, Combinatorica., 1 (1981), pp. 169-197.
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[5] M. Gr"otschel, L. Lov'asz, and A. Schrijver, Geometric algorithms and combinatorial optimization, Springer-Verlag., Berlin Heidelberg, 2012.
5
[6] S. Hanifehnezhad and A. Dolati, Gomory Hu Tree and Pendant Pairs of a Symmetric Submodular System, Lecture Notes in Comput. Sci., 10608 (2017), pp. 26-33.
6
[7] S. Iwata, L. Fleischer, and S. Fujishige, A combinatorial strongly polynomial algorithm for minimizing submodular functions, J. ACM., 48 (2001), pp. 761-777.
7
[8] S. Jegelka and J. Bilmes, Cooperative cuts for image segmentation, Technical Report, University of Washington, Seattle, 2010.
8
[9] A. Krause and D. Golovin, Submodular function maximization, in: Tractability: Practical Approaches to Hard Problems, Cambridge Univ. Press., Cambridge, 2014, 71-104.
9
[10] Y.T. Lee, A. Sidford, and S.C. Wong, A faster cutting plane method and its implications for combinatorial and convex optimization, in: Foundations of Computer Science (FOCS), 2015 IEEE 56th Annual Symposium, Berkeley, California, 2015, 1049-1065.
10
[11] S.T. McCormick, Submodular function minimization, Handbooks Oper. Res. Management Sci., 12 (2005), pp. 321-391.
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[12] H. Nagamochi, Minimum degree orderings, Algorithmica., 56 (2010), pp. 17–34.
12
[13] H. Nagamochi and T. Ibaraki, A note on minimizing submodular functions, Inform. Process. Lett., 67 (1998), pp. 239-344.
13
[14] N. Nisan, T. Roughgarden, E. Tardos, and V.V. Vazirani, Algorithmic game theory, Cambridge Univ. Press., New York, USA, 2007.
14
[15] J.B. Orlin, A faster strongly polynomial time algorithm for submodular function minimization, Math. Program., 118 (2009), pp. 237-251.
15
[16] M. Queyranne, Minimizing symmetric submodular functions, Math. Program., 82 (1998), pp. 3-12.
16
[17] A. Schrijver, A combinatorial algorithm minimizing submodular functions in strongly polynomial time, J. Combin. Theory Ser. B., 80 (2000), pp. 346-355.
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[18] A. Schrijver, Combinatorial optimization: polyhedra and efficiency, Springer-Verlag., Berlin Heidelberg, 2003.
18
[19] D.M. Topkis, Supermodularity and complementarity, Princeton Univ. Press., Princeton, 2011.
19
ORIGINAL_ARTICLE
A New Common Fixed Point Theorem for Suzuki Type Contractions via Generalized $\Psi$-simulation Functions
In this paper, a new stratification of mappings, which is called $\Psi$-simulation functions, is introduced to enhance the study of the Suzuki type weak-contractions. Some well-known results in weak-contractions fixed point theory are generalized by our researches. The methods have been appeared in proving the main results are new and different from the usual methods. Some suitable examples are furnished to demonstrate the validity of the hypothesis of our results and reality of our generalizations.
https://scma.maragheh.ac.ir/article_36368_2759917fb5f016efd9411aa212341008.pdf
2019-10-01
129
148
10.22130/scma.2018.78315.359
Common fixed point
Suzuki type contractions
Generalized $Psi$-simulation functions
Gholamreza
Heidary Joonaghany
1
Department of Mathematics, Faculty of Science, Science and Research Branch, Islamic Azad University, Tehran, Iran.
AUTHOR
Ali
Farajzadeh
farajzadehali@gmail.com
2
Department of Mathematics, Faculty of Science, Razi University, Kermanshah 67149, Iran.
LEAD_AUTHOR
Mahdi
Azhini
mahdi.azhini@gmail.com
3
Department of Mathematics, Faculty of Science, Science and Research Branch, Islamic Azad University, Tehran, Iran.
AUTHOR
Farshid
Khojasteh
f-khojaste@iau-arak.ac.ir
4
Department of Mathematics, Faculty of Science, Arak Branch, Islamic Azad University, Arak, Iran.
AUTHOR
[1] Ya.I. Alber and S. Guerre-Delabriere, Principles of weakly contractive maps in Hilbert spaces, in: I. Gohberg, Yu. Lyubich (Eds.), New Results in Operator Theory, in Advances and Appl., 98 (1997), pp. 7-22.
1
[2] H. Argoubi, B. Samet, and C. Vetro, Nonlinear contractions involving simulation functions in a metric space with a partial order, J. Nonlinear Sci. Appl., 8 (2015), pp. 1082-1094.
2
[3] A.D. Arvanitakis, A proof of the generalized Banach contraction conjecture, Proc. Amer. Math. Soc., 131 (2003), pp. 3647–-3656.
3
[4] S. Banach, Sur les operations dans les ensembles abstraits et leurs applications aux equations integrales, Fund. Math., 3 (1922), pp. 133-181.
4
[5] V. Berinde, Approximating fixed points of weak $varphi$-contractions, Fixed Point Theory, 4 (2003), pp. 131-142.
5
[6] D. Doric, Common fixed point for generalized $(psi - varphi)$-weak contraction, Appl. Math. Lett., 22 (2009), pp. 1896-1900.
6
[7] D. Doric, Z. Kadelburg, and S. Radenovic, Edelstein-Suzuki-type fixed point results in metric and abstract metric spaces, Nonlinear Anal., 75 (2012), pp. 1927-1932.
7
[8] D. Doric and R. Lazovic, Some Suzuki-type fixed point theorems for generalized multivalued mappings and applications, Fixed Point Theory Appl., 2011 (2011), 13 pages.
8
[9] P.N. Dutta and B.S. Choudhary, A generalization of contraction principle in metric spaces, Fixed Point Theory Appl., 2008 (2008), 8 pages.
9
[10] F. Khojasteh, S. Shukla, and S. Radenovic, A new approach to the study of fixed point theorems via simulation functions, Filomat, 29 (2015), pp. 1189-1194.
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[11] M. Kikkawa and T. Suzuki, Some notes on fixed point theorems with constants, Bull. Kyushu Inst. Technol. Pure Appl. Math., 56 (2009), pp. 11-18.
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[12] M. Kikkawa and T. Suzuki, Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal., 69 (2008), pp. 2942-2949.
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[13] W. Kirk and B. Sims, Handbook of metric fixed point theory, Springer Science & Business Media., 2001.
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[14] A. Meir and E. Keeler, A theorem on contraction mappings, J. Math. Anal. Appl., 28 (1969), pp. 326-329.
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[15] A. Nastasi and P. Vetro, Fixed point results on metric and partial metrric spaces via simulations functions, J. Nonlinear Sci. Appl.,
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8 (2015), pp. 1059-1069.
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[16] M. Olgun, O. Bicer, and T. Alyildiz, A new aspect to Picard operators with simulation functions, Turk. J. Math., 40 (2016), pp. 832-837.
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[17] K.P.R. Rao, K.P.K. Rao, and H. Aydi, A Suzuki type unique common fixed point theorem for hybrid pairs of maps under a new condition in partial metric spaces, Mathematical Sciences, 7 (2013), 8 pages.
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[18] B.E. Rhodes, Some theorems on weakly contractive maps, Nonlinear Anal., 47 (2001), pp. 2683-2693.
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[19] A. Roldan, E. Karapinar, C. Roldan, and J. Martinez-Moreno, Coincidence point theorems on metric spaces via simulation functions, J. Comput. Appl. Math., 275 (2015), pp. 345–-355.
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[20] S.L. Singh, S.N. Mishra, Renu Chugh, and Raj Kamal, General common fixed point theorems and applications, J. Appl. Math., 2012 (2012), 14 pages.
21
[21] S.L. Singh, R. Kamal, M. De La Sen, and Renu Chugh, A Fixed Point Theorem for Generalized Weak Contractions, Filomat, 29 (2015), pp. 1481-1490.
22
[22] S.L. Singh, Renu Chugh, and Raj Kamal, Suzuki type common fixed point theorems and applications, Fixed Point Theory, 14 (2) (2013), pp. 497-506.
23
[23] T. Suzuki, A generalized Banach contraction principle that Characterizes metric completeness, Proc. Amer. Math. Soc., 136 (2008), pp. 1861-1869.
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[24] T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 (11) (2009), pp. 5313-5317.
25
[25] Q. Zhang and Y. Song, Fixed point theory for generalized $(psi - varphi)$-weak contractions, Appl. Math. Lett., 22 (2009), pp. 75-78.
26
ORIGINAL_ARTICLE
Coefficient Bounds for Analytic bi-Bazilevi\v{c} Functions Related to Shell-like Curves Connected with Fibonacci Numbers
In this paper, we define and investigate a new class of bi-Bazilevic functions related to shell-like curves connected with Fibonacci numbers. Furthermore, we find estimates of first two coefficients of functions belonging to this class. Also, we give the Fekete-Szegoinequality for this function class.
https://scma.maragheh.ac.ir/article_36054_c859e3f5aa44c8ed0ef018ea37bd44a7.pdf
2019-10-01
149
160
10.22130/scma.2018.82266.401
Bi-Bazilevic function
Analytic function
Shell-like curve
Fibonacci numbers
Hatun Ozlem
Guney
ozlemg@dicle.edu.tr
1
Dicle University, Department of Mathematics, Science Faculty, TR-21280 Diyarbakir, Turkey.
LEAD_AUTHOR
[1] I.E. Bazilevic, On a case of integrability in quadratures of the Lowner-Kufarev equation, Math. Sb., 37(1955), pp. 471-476.
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[2] D.A. Brannan, J. Clunie, and W.E. Kirwan, Coefficient estimates for a class of star-like functions, Canad. J. Math., 22 (1970), pp. 476-485.
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[4] P.L. Duren, Univalent Functions, In: Grundlehren der Mathematischen Wissenschaften, Band 259, New York, Berlin, Heidelberg and Tokyo, Springer-Verlag, 1983.
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[5] J. Dziok, R.K. Raina, and J. Sokol, On a class of starlike functions related to a shell-like curve connected with Fibonacci numbers, Math. and Computer Modelling, 57 (2013), pp. 1203-1211.
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[6] J. Dziok, R.K. Raina, and J. Sokol, On $alpha-$convex functions related to a shell-like curve connected with Fibonacci numbers, Appl. Math. Comp., 218 (2011), pp. 996-1002.
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[8] M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc., 18 (1967), pp. 63-68.
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[9] X.F. Li and A.P. Wang, Two new subclasses of bi-univalent functions, International Mathematical Forum, 7 (2012), pp. 1495--1504.
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[10] Ch. Pommerenke, Univalent Functions, Math. Math, Lehrbucher, Vandenhoeck and Ruprecht, Gottingen, 1975.
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[11] R.K. Raina and J. Sokol, Fekete-Szego problem for some starlike functions related to shell-like curves, Math. Slovaca, 66 (2016), pp. 135-140.
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[13] H.M. Srivastava and D. Bansal, Coefficient estimates for a subclass of analytic and bi-univalent functions, J. Egyptian Math. Soc., 23 (2015), pp. 242-246.
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[14] H.M. Srivastava, S. Bulut, M. Caglar, and N. Yagmur, Coefficient estimates for a general subclass of analytic and bi-univalent functions, Filomat, 27 (2013), pp. 831-842.
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[17] H.M. Srivastava, S. Gaboury, and F. Ghanim, Coefficient estimates for some subclasses of m-fold symmetric bi-univalent functions, Acta Univ. Apulensis Math. Inform., 23(2015), pp. 153-164.
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[19] Srivastava, S. Sivasubramanian, and R. Sivakumar, Initial coefficient bounds for a subclass of m-fold symmetric bi-univalent functions, Tbilisi Math. J., 7(2014), pp. 1-10.
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[21] H. Tang, H.M. Srivastava, S. Sivasubramanian, and P. Gurusamy, The Fekete-Szego functional problems for some subclasses of m-fold symmetric bi-univalent functions, J. Math. Inequal., 10 (2016), pp. 1063-1092.
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[23] P. Zaprawa, On the Fekete-Szego problem for classes of bi-univalent functions, Bull. Belg. Math. Soc. Simon Stevin, 21(2014), pp.169-178.
23