2019
16
1
0
160
1

A Proximal Point Algorithm for Finding a Common Zero of a Finite Family of Maximal Monotone Operators
https://scma.maragheh.ac.ir/article_36660.html
10.22130/scma.2019.100821.542
1
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.
0

1
15


Mohsen
Tahernia
Department of Mathematics, Faculty of Science, Arak University, 3815688349, Arak, Iran.
Iran
m.taherniamath@gmail.com


Sirous
Moradi
Department of Mathematics, Faculty of Science, Arak University, 3815688349, Arak, Iran.
Iran
sirousmoradi@gmail.com


Somaye
Jafari
Department of Mathematics, Faculty of Science, Arak University, 3815688349, Arak, Iran.
Iran
s.jafari.math@gmail.com
Maximal monotone operator
Proximal point algorithm
Nonexpansive map
Resolvent operator
[[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. 283301.##[2] H.H. Bauschke, E. Matouskova, and S. Reich, Projection and proximal point methods: convergence results and counterexamples, Nonlinear Anal. (TMA), 56 (2004), pp. 715738.##[3] O.A. Boikanyo and G. Morosanu, A contraction proximal point algorithm with two monotone operators, Nonlinear Anal. (TMA), 75 (2012), pp. 56865692.##[4] O.A. Boikanyo and G. Morosanu, On the method of alternating resolvents, Nonlinear Anal. (TMA), 74 (2011), pp. 51475160.##[5] O.A. Boikanyo and G. Morosanu, Strong convergence of the method of alternating resolvents, J. Nonlinear Convex Anal., 14 (2013), pp. 221229.##[6] O.A. Boikanyo and G. Morosanu, The method of alternating resolvents revisited, Numer. Funct. Anal. Optim., 33 (2012), pp. 12801287.##[7] L.M. Bregman, The method of successive projection for finding a common point of convex sets, Sov. Math. Dokl., 6 (1965), pp. 688692.##[8] K. Goebel and S. Reich, Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings, Marcel Dekker, New York and Basel, 1984.##[9] H. Hundal, An alternating projection that does not converge in norm, Nonlinear Anal. (TMA), 57 (2004), pp. 3561.##[10] E. Kopecka and S. Reich, A note on the von Neumann alternating projections algorithm, J. Nonlinear Convex Anal., 5 (2004), pp. 379386.##[11] P.E. Mainge, Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization, SetValued Anal., 16 (2008), pp. 899912.##[12] E. Matouskova and S. Reich, The Hundal example revisited, J. Nonlinear Convex Anal., 4 (2003), pp. 411427.##[13] G. Morosanu, Nonlinear Evolution Equations and Applications, Reidel, Dordrecht, 1988.##[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. 3746.##[15] N. Nimit, A.P. Farajzadeh, and N. Petrot, Adaptive subgradient method for the split quasiconvex feasibility problems, Optimization, 65 (2016), pp. 18851898.##[16] H.K. Xu, A regularization method for the proximal point algorithm, J. Glob. Optim., 36 (2006), pp. 115125.##[17] P. Yatakoat, A new approximation method for common fixed points of a finite family of nonexpansive nonself mappings in Banach spaces, Int. J. Nonlinear Anal. Appl., 9 (2018), pp. 223234.##]
1

Diameter Approximate Best Proximity Pair in Fuzzy Normed Spaces
https://scma.maragheh.ac.ir/article_36659.html
10.22130/scma.2018.83850.420
1
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 wellknown 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.
0

17
34


Seyed Ali Mohammad
Mohsenialhosseini
Faculty of Mathematics, Yazd University, Yazd, Iran and Department of Mathematics, ValieAsr University of Rafsanjan, Rafsanjan, Iran.
Iran
mohsenhosseini@yazd.ac.ir


Morteza
Saheli
Department of Mathematics, ValieAsr University of Rafsanjan, Rafsanjan, Iran.
Iran
saheli@vru.ac.ir
Cyclic maps
$alpha$asymptotically regular
$F$Kannan operator
Fuzzy diameter
[[1] T. Bag and S.K. Samanta, Finite dimensional fuzzy normed linear spaces, J. Fuzzy Math., 11 (2003), pp. 687705.##[2] T. Bag and S.K. Samanta, Fuzzy bounded linear operators, Fuzzy Sets and Systems, 151 (2005), pp. 513547.##[3] T. Bag and S.K. Samanta, Some fixed point theorems in fuzzy normed linear spaces, Inf. Sci., 177 (2007), pp. 32713289.##[4] M. Berinde, Approximate fixed point theorems, Mathematica, LI (1) (2006).##[5] V. Berinde, Approximating fixed points of weak contractions using the Picard iteration, Nonlinear Anal. Forum, 9 (2004).##[6] V. Berinde, On the approximation of fixed points of weak contractive mappings, Math., 19 (2003), pp. 722.##[7] S.K. Chatterjea, Fixedpoint theorems, C.R. Acad. Bulgare Sci. 25 (1972), pp. 727730.##[8] S.C. Cheng and J.N. Mordeson, Fuzzy linear operator and fuzzy normed linear spaces, Bull. Calcutta Math. Soc., 86 (1994), pp. 429436.##[9] A. Chitra and P.Y. Mordeson, Fuzzy linear operators and fuzzy normed linear spaces, Bull. Calcutta Math. Soc., 74 (1969), pp. 660665.##[10] Lj. B. Ciric, A generalization of Banach’s contraction principle, Proc. Am. Math. Soc., 45 (1974), pp. 267273.##[11] C. Felbin, Finite dimensional fuzzy normeded linear spaces, Fuzzy Sets and Systems, 48 (1992), pp. 239248.##[12] O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy Sets and Systems, 12 (1984), pp. 215229.##[13] R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc., 10 (1968), pp. 7176.##[14] A.K. Katsaras, Fuzzy topological vector spaces II, Fuzzy Sets and Systems, 12 (1984), pp. 143154.##[15] I. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica, 11 (1975), pp. 326334.##[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.##[17] S.A.M. Mohsenalhosseini, Approximate best proximity pairs in metric space for Contraction Maps, Advances in Fixed Point Theory, 4 (2014), pp. 310324.##[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.##[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. 135142.##]
1

Fixed Point Theory in $varepsilon$connected Orthogonal Metric Space
https://scma.maragheh.ac.ir/article_36366.html
10.22130/scma.2018.72368.289
1
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.
0

35
46


Madjid
Eshaghi Gordji
Department of Mathematics, Semnan University, P.O. Box 35195363, Semnan, Iran.
Iran
meshaghi@semnan.ac.ir


Hasti
Habibi
Department of Mathematics, Semnan University, Semnan, Iran.
Iran
hastihabibi1363@gmail.com
Fixed point
$varepsilon$connected
Orthogonal set
solution
Metric space
Analytic function
[[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. 465477.##[2] I. Beg and A.R. Butt, Fixed point of setvalued graph contractive mappings, J. Inequa. Appl., (2013), 2013:252.##[3] M. Edelstein, An extension of Banach's contraction principle, Proc. Amer. Math. Soc., 12 (1961), pp. 710.##[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. 148151.##[5] M. Eshaghi Gordji, H. Baghani, H. Khodaei, and M. Ramezani, Generalized multi valued contraction mappings, J. Comput. Anal. Appl., 13 (2011), pp. 730733.##[6] M. Eshaghi Gordji, H. Baghani, H. Khodaei, and M. Ramezani, Geraghty's fixed point theorem for special multivalued mappings, Thai. J. Math., 10 (2012), pp. 225231.##[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. 569578.##[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. 103111.##[9] N. Mehmood, A. Azam, and S. Aleksic, Topological vectorspace valued cone Banach spaces, Int. J. Anal. Appl., 6 (2014), pp. 205219.##[10] M. Ramezani, Orthogonal metric space and convex contractions, Int. J. Nonlinear Anal. Appl., 6 (2015), pp. 127132.##[11] M. Ramezani, H. Baghani, Contractive gauge functions in strongly orthogonal metric spaces, Int. J. Nonlinear Anal. Appl., 8 (2017), pp. 2328.##[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. 3848.##]
1

$p$adic Dual Shearlet Frames
https://scma.maragheh.ac.ir/article_34965.html
10.22130/scma.2018.77684.355
1
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 $L^2left(Q_p^{2}right)$. The discrete $p$adic shearlet frames for $L^2left(Q_p^{2}right)$ is discussed. Also we prove that the frame operator $S$ associated with the group $G_p$ of all with the shearlet frame $SHleft( psi; Lambdaright)$ 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 $L^2left(Hright)^{vee}$ of $L^2left(Q_p^{2}right)$. Finally we give a necessary condition for two functions in $L^2left(Q_p^{2}right)$ to generate a padic dual shearlet tight frame via admissibility.
0

47
56


Mahdieh
Fatemidokht
Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
Iran
fatemidokht@gmail.com


Ataollah
Askari Hemmat
Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
Iran
askari@uk.ac.ir
$p$adic numbers
Dual frame
$p$adic shearlet system
$p$adic dual tight frame
[[1] O. Christensen, An introduction to Frames and Riesz Bases, Birkhauser, Boston, 2003.##[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. 157181.##[3] M. Fatemidokht and A. Askari Hemmat, $P$adic shearlets, Wavel. Linear Algebra, to appear##[4] B. Han, On dual wavelet tight frames, Appl. Comput. Harmon. Anal., 4 (1997), pp. 380413.##[5] G. Kutyniok and D. Labate, Construction of regular and irregular shearlet frames, J. Wavelet Theory Appl., 1 (2007), pp. 110.##[6] G. Kutyniok and D. Labate, Shearlets: Multiscle Analysis for Multivariate Data, Birkhauser. Basel, 2012.##[7] V.S. Valdimirov, I.V. Volovich, and E.I. Zelenov, $p$Adic Analysis and Mathematical Physics, World Scientific, Singapore, 1994.##]
1

Simple Construction of a Frame which is $epsilon$nearly Parseval and $epsilon$nearly Unit Norm
https://scma.maragheh.ac.ir/article_36056.html
10.22130/scma.2018.79613.374
1
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 $left{f_kright}_{k=1}^infty$ and $left{Tf_kright}_{k=1}^infty$ are $epsilon$nearly equal frame operators, where $left{f_kright}_{k=1}^infty$ is a frame for $mathcal{H}$. Finally, we introduce and characterize all operator dual Parseval frames of a given Parseval frame.
0

57
67


Mohammad Ali
Hasankhani Fard
Department of Mathematics ValieAsr University, Rafsanjan, Iran.
Iran
m.hasankhani@vru.ac.ir
Frame
Parseval frame
$epsilon$nearly Parseval frame
$epsilon$nearly equal frame operators
Operator dual Parseval frames
[[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. 109132.##[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.##[3] B.G. Bodmann and P.G. Casazza, The road to equalnorm Parseval frames, J. Funct. Anal., 258 (2010), pp. 397420.##[4] J. Cahill, P.G. Casazza, and G. Kutyniok, Operators and frames, J. Operator Theory., 70 (2013), pp. 145164.##[5] P.G. Casazza and J. Kovacevic, Equalnorm tight frames with erasures, Adv. Comput. Math., 18 (2003), pp. 387430.##[6] O. Christensen, An Introduction to Frames and Riesz Bases, Birkhauser., Boston, Basel, Berlin, 2002.##[7] O. Christensen and Y. Eldar, Oblique dual frames and shiftinvariant spaces, Appl. Comput. Harmon. Anal., 17 (2004), pp. 4868.##[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. 7790.##[9] D. Freeman and D. Speegle, The discretization problem for continuous frames., https://arxiv.org/abs/1611.06469.##[10] V.K. Goyal, J. Kovacevic, and J.A. Kelner, Quantized frame expansions with erasures, Appl. Comput. Harmon. Anal., 10 (2001), pp. 203233.##[11] C. Heil, Y.Y. Koo, and J.K. Lim, Duals of frame sequences, Acta Appl. Math., 107 (2008), pp. 7590.##[12] C. Heil and D. Walnut, Continuous and discrete wavelet transform, SIAM Rev., 31 (1969), pp. 628666.##[13] A.A. Hemmat and J.P. Gabardo, Properties of oblique dual frames in shiftinvariant systems, J. Math. Anal. Appl., 356 (2009), pp. 346354.##[14] S. Li and H. Ogawa, Pseudo duals of frames with applications, Appl. Comput. Harmon. Anal., 11 (2001), pp. 289304.##[15] R. Young, An Introduction to Nonharmonic Fourier Series, Academic Press., New York, 1980.##]
1

Coefficient Estimates for Some Subclasses of Analytic and BiUnivalent Functions Associated with Conic Domain
https://scma.maragheh.ac.ir/article_36057.html
10.22130/scma.2018.87581.449
1
The main objective of this investigation is to introduce certain new subclasses of the class $Sigma $ of biunivalent functions by using concept of conic domain. Furthermore, we find nonsharp estimates on the first two TaylorMaclaurin 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.
0

69
81


Muhamamd
Tahir
Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan.
Iran
tahirmuhammad778@gmail.com


Nazar
Khan
Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan.
Iran
nazarmaths@gmail.com


Qazi Zahoor
Ahmad
Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan.
Iran
zahoorqazi5@gmail.com


Bilal
Khan
Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan.
Iran
bilalmaths789@gmail.com


Gul Mehtab
Khan
Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan.
Iran
mehtabmaths789@gmail.com
Univalent function
Analytic function
Biunivalent function
Subordination between analytic functions
Starlike and strongly starlike functions
Conic domain
[[1] N.I. Ahiezer, Elements of theory of elliptic functions, Moscow, 1970.##[2] G.D. Anderson, M.K. Vamanamurthy, and M.K. Vourinen, Conformal invariants, inequalities and quasiconformal maps, WileyInterscience, 1997.##[3] M. Arif, J. Dziok, M. Raza, and J. Sokol, On products of multivalent closetostar functions, J. Ineq. appl., 2015 (2015), pp. 114.##[4] S.Z.H. Bukhari, M. Nazir, and M. Raza, Some generalisations of analytic functions with respect to 2ksymmetric conjugate points, Maejo Int. J. Sci. Technol., 2016, pp. 10, 112.##[5] P.L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften (Fundamental Principles of Mathematical Science), vol. 259, SpringerVerlag, New York, Berlin, 1983.##[6] B.A. Frasin, Coefficient bounds for certain classes of biunivalent functions, Hacettepe J. Math. Stat., 43 (2014), pp. 383389.##[7] S. Hussain, N. Khan, S. Khan, and Q.Z. Ahmad, On a subclass of analytic and biunivalent functions, Southeast Asian Bull. Math., article in press.##[8] S. Kanas and A. Wisniowska, Conic regions and kuniform convexity, J. Comput. Appl. Math., 105 (1999), pp. 327336.##[9] S. Kanas and A. Wisniowska, Conic domains and starlike functions, Rev. Roumaine Math. Pures Appl., 45 (2000), pp. 647657.##[10] S. Kanas, Coefficient estimates in subclasses of the Caratheodory class related to conical domains, Acta Math. Univ. Comenian., 74 (2005), pp. 149161.##[11] N. Khan, B. Khan, Q.Z. Ahmad, and S. Ahmad, Some Convolution Properties of Multivalent Analytic Functions, AIMS Math., 2 (2017), pp. 260268.##[12] N. Khan, Q.Z. Ahmad, T. Khalid, and B. Khan, Results on spirallike $p$valent functions, AIMS Math., 3 (2018), pp. 1220.##[13] N. Khan, A. Khan, Q.Z. Ahmad, B. Khan, and S. Khan, Study of multivalent spirallike Bazilevic functions AIMS Math., 3 (2018), pp. 353364.##[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. 689701.##[15] K.I. Noor, On a generalization of uniformly convex and related functions, Comput. Math. Appl., 61 (2011), pp. 117125.##[16] K.I. Noor, M. Arif, and M.W. UlHaq, On $k$uniformly closetoconvex functions of complex order, Appl. Math. Comput., 215 (2009), pp. 629635.##[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. 819.##[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. 114.##[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. 18.##[20] K.I. Noor and N. Khan, Some convolution properties of a subclass of pvalent functions, Maejo Int. J. Sci. Technol., 9 (2015), pp. 181192.##[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. 137149.##[22] M. Obradovic and S. Owa, Some sufficient conditions for strongly starlikeness, Int. J. Math. Math. Sci., 24 (2000), pp. 643647.##[23] M. Raza, M. U Din, and S.N. Malik, Certain geometric properties of normalized wright functions, J. Func. Spaces, 2016 (2016), 9 pages.##[24] W. Rogosinski, On the coefficients of subordinate functions, Proc. Lond. Math. Soc., 48 (1943), pp. 4882.##[25] H.M. Srivastava, A.K. Mishra, and P. Gochhayat, Certain subclasses of analytic and biunivalent functions, Appl. Math. Lett., 23 (2010), pp. 11881192.##[26] H.M. Srivastava, S. Bulut, M. Caglar, and N. Yagmur, Coefficient estimates for a general subclass of analytic and biunivalent functions, Filomat, 27 (2013), pp. 831842.##[27] H.M. Srivastava, and D. Bansal, Coefficient estimates for a subclass of analytic and biunivalent functions, J. Egyptian Math. Soc., 23 (2015), pp. 242246.##[28] H.M. Srivastava, G. Murugusundaramoorthy, and N. Magesh, Certain subclasses of biunivalent functions associated with the Hohlov operator, Global J. Math. Anal., 1 (2013), pp. 6773.##[29] W.UlHaq and S. Manzar, Coefficient Estimates for Certain Subfamilies of ClosetoConvex Functions of Complex Order, Filomat, 30 (2016), pp. 99103.##[30] W. UlHaq, A. Nazneen, and N. Rehman, Coefficient estimates for certain subfamilies of closetoconvex functions of complex order, Filomat, 28 (2014), pp. 11391142.##[31] W. UlHaq, A. Nazneen, M. Arif, and N. Rehman, Coefficient estimate of certain subfamily of close to convex functions, J. Comput. Anal. Appl., 16 (2013), pp. 133138.##[32] W. UlHaq and S. Mahmmod, Certain properties of a subfamily of closetoconvex functions related to conic regions, Abst. Appl. Anal., Article ID: 847287, 2013 (2013), 6 pp.##[33] Q.H. Xu, H.G. Xiao, and H. M. Srivastava, A certain general subclass of analytic and biunivalent functions and associated coefficient estimate problems, Appl. Math. Comput., 218 (2012),##]
1

$L_{p;r} $ spaces: Cauchy Singular Integral, Hardy Classes and RiemannHilbert Problem in this Framework
https://scma.maragheh.ac.ir/article_36058.html
10.22130/scma.2018.81285.391
1
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{Aleft(tright)e^{{mathop{rm int}} }; Bleft(tright)e^{{mathop{rm int}} } right}_{nin 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 RiemannHilbert problem has a unique solution in corresponding Hardy class ${ H}_{p;r}^{+} times { H}_{p;r}^{+} $.
0

83
91


Ali
Huseynli
Department of Mathematics, Khazar University, AZ1096, Baku, Azerbaijan and Department of Nonharmonic analysis, Institute of Mathematics and Mechanics of NAS of Azerbaijan, AZ1141, Baku, Azerbaijan.
Iran
alihuseynli@gmail.com


Asmar
Mirzabalayeva
Department of Nonharmonic analysis", Institute of Mathematics and Mechanics of NAS of Azerbaijan, AZ1141, Baku, Azerbaijan.
Iran
esmer26@mail.ru
Function space
Hardy class
singular integral
RiemannHilbert problem
[[1] D.R. Adams, Morrey spaces, Springer, 2016.##[2] B.T. Bilalov, On isomorphisms of two bases in $L_{p}$, Fundam. Prikl. Mat., 1 (1995), pp. 10911094.##[3] B.T. Bilalov, T.B. Gasymov, and A.A. Guliyeva, On solvability of Riemann boundary value problem in MorreyHardy classes, Turkish J. Math., 40 (2016), pp. 10851101.##[4] B.T. Bilalov and Z.G. Guseynov, Basicity of a system of exponents with a piecewise linear phase in variable spaces, Mediterr. J. Math., 9 (2012), pp. 487498.##[5] B.T. Bilalov and Z.G. Guseynov, On the basicity from exponents in Lebesgue spaces with variable exponents, TWMS J. Pure Appl. Math., 1 (2010), pp. 1423.##[6] B.T. Bilalov and A.A. Quliyeva, On basicity of exponential systems in Morreytype spaces, Internat. J. Math., 25 (2014), 10 pages.##[7] B.T. Bilalov and Z.Q. Quseynov, Bases from exponents in Lebesgue spaces of functions with variable summability exponent, Trans. Natl. Acad. Sci. Azerb. Ser. Phys.Tech. Math. Sci., XXVIII(1) (2008), pp. 4348.##[8] J.B. Conway, Functions of one complex variable, II, SpringerVerlag, 2012.##[9] D.V. CruzUribe and A. Fiorenza, Variable Lebesgue spaces: Foundations and Harmonic Analysis, Springer, 2013.##[10] L. Diening, P. Harjulehto, P. Hasto, and M. Ruzicka, Lebesgue and Sobolev spaces with variable exponents, SpringerVerlag, Berlin, 2017.##[11] G.M. Goluzin, Geometric theory of functions of complex variables, AMS Trans. Math. Monographes, 29, 1969.##[12] D.M. Israfilov and N.P. Tozman, Approximation in MorreySmirnov classes, Azerb. J. Math., 1 (2011), pp. 99113.##[13] Y. Katznelson, Sets of uniqueness for some classes of trigonometric series, Bull. Amer. Math. Soc., 70 (1964), 722723.##[14] V. Kokilashvili, A. Meskhi, H. Rafeiro, and S. Samko, Integral Operators in Nonstandard function spaces, Birkhauser, 2, 2016.##[15] P. Koosis, Introduction to $H_p$ spaces, 2nd edition, CUP, 1998.##[16] S.M. Nikolski, Approximation of functions of several variables and embedding theorems, Nauka, Moscow, 1969.##]
1

Generalized $F$contractions in Partially Ordered Metric Spaces
https://scma.maragheh.ac.ir/article_36059.html
10.22130/scma.2018.81871.398
1
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.
0

93
104


Seyede Samira
Razavi
Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran.
Iran
srazavi@mail.kntu.ac.ir


Hashem
Parvaneh Masiha
Faculty of Mathematics, K. N. Toosi University of Technology, P.O. Box 163151618, Tehran, Iran.
Iran
masiha@kntu.ac.ir
Fixed point
$F$contraction
Ordered weakly $F$contraction
Generalized $F$contraction
$acute{mathrm{C}}$iri$acute{mathrm{c}}$ type mappings
[[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. 15201526.##[2] O. Acar, G. Durmaz, and G. Minak, Generalized multivalued Fcontractions on complete metric spaces, Bull. Iranian Math. Soc., 40 (2014), pp. 14691478.##[3] R.P. Agarwal, M.A. ElGebeily, and D. O’Regan, Generalized contractions in partially ordered metric spaces, Appl. Anal., 87 (2008), pp. 109116.##[4] S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fund. Math., 3 (1922), pp. 133181.##[5] Lj.B. Ciric, A generalization of Banach’s contraction principle, Proc. Amer. Math. Soc., 45 (1974), pp. 267273.##[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. 57845789.##[7] W.S. Du, Some new results and generalizations in metric fixed point theory, Nonlinear Anal., 73 (2010), pp. 14391446.##[8] G. Durmaz, G. Mınak, and I. Altun, Fixed points of ordered Fcontractions, Hacet. J. Math. Stat., 45 (2016), pp. 1521.##[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.##[10] J. Matkowski, Fixed point theorems for mappings with a contractive iterate at a point, Proc. Amer. Math. Soc., 62 (1977), pp. 344348.##[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. 11431151##[12] H.K. Nashine and I. Altun, A common fixed point theorem on ordered metric spaces, Bull. Iranian Math. Soc., 38 (2012), pp. 925934.##[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. 223239.##[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. 22052212.##[15] D. O’Regan and A. Petrusel, Fixed point theorems for generalized contractions in ordered metric spaces, J. Math. Anal. Appl., 341 (2008), pp. 12411252.##[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. 14351443.##[17] B.E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal., 47 (2001), pp. 26832693.##[18] A. Tarski, A latticetheoretical fixpoint theorem and its applications, Pacific J. Math., 5 (1955), pp. 285309., MR0074376.##[19] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 94 (2012), 6 pages.##]
1

Some Properties of $ ast $frames in Hilbert Modules Over ProC*algebras
https://scma.maragheh.ac.ir/article_36278.html
10.22130/scma.2018.75253.328
1
In this paper, by using the sequence of adjointable operators from proC*algebra $ mathcal{A} $ into a Hilbert $ mathcal{A} $module $ E $. We introduce frames with bounds in proC*algebra $ mathcal{A} $. New frames in Hilbert modules over proC*algebras are called standard $ ast $frames of multipliers. Meanwhile, we study several useful properties of standard $ ast $frames in Hilbert modules over proC*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 proC*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 proC*algebras are studied.
0

105
117


Mona
Naroei Irani
Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran.
Iran
m.naroei.math@gmail.com


Akbar
Nazari
Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
Iran
nazari@uk.ac.ir
Hilbert modules over proC*algebras
Standard $ ast $frame of multipliers
$ ast $frame operator
Pre$ ast $frame
[[1] M. Azhini and N. Haddadzadeh, Fusion frames in Hilbert modules over proC*algebras, Int. J. Industrial Math., 5 (2013), pp. 109118.##[2] P.G. Casazza and G. Kutyniok, Frames of subspaces, Contemp. Math., Amer. Math. Soc., 345 (2004), pp. 87113.##[3] I. Daubechies, A. Grossmann, and Y. Meyer, Painless nonorthogonal expansions, J. Math. Phys., 27 (1986), pp. 12711283.##[4] R.J. Duffin and A.C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc., 72 (1952), pp. 341366.##[5] M. Frank and D.R. Larson, Frames in Hilbert C*modules and C*algebras, J. Operator Theory., 48 (2002), pp. 273314.##[6] N. Haddadzadeh, Gframes in Hilbert proC*modules, Int. Electron. J. Pure Appl. Math., 105 (2015), pp. 727743.##[7] M. Joita, Hilbert Modules Over Locally C*Algebras, University of Bucharest Press, ISBN 9737371283, 2006.##[8] M. Joita, On frames in Hilbert modules over proC*algebras, Topology and its Applications., 156 (2008), pp. 8392.##[9] A. Khosravi and B. Khosravi, Fusion frames and gframes in Hilbert C*modules, Int. J. Wavelets Multiresolution. Inf., 6 (2008), pp. 433466.##[10] W.L. Paschke, Inner product modules over B*algebras, Trans. Amer. Math. Soc., 182 (1973), pp. 443468.##[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. 15571564.##[12] W. Sun, Gframes and gRiesz bases, J. Math. Anal. Appl., 322 (2006), pp. 437452.##]
1

Some Results about the Contractions and the Pendant Pairs of a Submodular System
https://scma.maragheh.ac.ir/article_36279.html
10.22130/scma.2018.91924.481
1
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 $left(V,fright)$ we construct a suitable sequence of $leftVright1$ 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.
0

119
128


Saeid
Hanifehnezhad
Department of Mathematics, Shahed University, Tehran, Iran.
Iran
saeid.hanifehnezhad@gmail.com


Ardeshir
Dolati
Department of Computer Science, Shahed University, Tehran, Iran.
Iran
dolati@shahed.ac.ir
Submodular system
Submodular optimization
Maximum adjacency ordering
Posimodular functions
Pendant pairs
stcut
[[1] D. Dadush, L.A. V'egh, and G. Zambelli, Geometric rescaling algorithms for submodular function minimization, in: Proc. 29th Annual ACMSIAM Symposium on Discrete Algorithms, New Orleans, Louisiana, USA, 2018, 832848.##[2] S. Fujishige, Submodular functions and optimization, Elsevier., Amesterdam, 2005.##[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. 11231145.##[4] M. Gr"otschel, L. Lov'asz, and A. Schrijver, The ellipsoid method and its consequences in combinatorial optimization, Combinatorica., 1 (1981), pp. 169197.##[5] M. Gr"otschel, L. Lov'asz, and A. Schrijver, Geometric algorithms and combinatorial optimization, SpringerVerlag., Berlin Heidelberg, 2012.##[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. 2633.##[7] S. Iwata, L. Fleischer, and S. Fujishige, A combinatorial strongly polynomial algorithm for minimizing submodular functions, J. ACM., 48 (2001), pp. 761777.##[8] S. Jegelka and J. Bilmes, Cooperative cuts for image segmentation, Technical Report, University of Washington, Seattle, 2010.##[9] A. Krause and D. Golovin, Submodular function maximization, in: Tractability: Practical Approaches to Hard Problems, Cambridge Univ. Press., Cambridge, 2014, 71104.##[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, 10491065.##[11] S.T. McCormick, Submodular function minimization, Handbooks Oper. Res. Management Sci., 12 (2005), pp. 321391.##[12] H. Nagamochi, Minimum degree orderings, Algorithmica., 56 (2010), pp. 17–34.##[13] H. Nagamochi and T. Ibaraki, A note on minimizing submodular functions, Inform. Process. Lett., 67 (1998), pp. 239344.##[14] N. Nisan, T. Roughgarden, E. Tardos, and V.V. Vazirani, Algorithmic game theory, Cambridge Univ. Press., New York, USA, 2007.##[15] J.B. Orlin, A faster strongly polynomial time algorithm for submodular function minimization, Math. Program., 118 (2009), pp. 237251.##[16] M. Queyranne, Minimizing symmetric submodular functions, Math. Program., 82 (1998), pp. 312.##[17] A. Schrijver, A combinatorial algorithm minimizing submodular functions in strongly polynomial time, J. Combin. Theory Ser. B., 80 (2000), pp. 346355.##[18] A. Schrijver, Combinatorial optimization: polyhedra and efficiency, SpringerVerlag., Berlin Heidelberg, 2003.##[19] D.M. Topkis, Supermodularity and complementarity, Princeton Univ. Press., Princeton, 2011.##]
1

A New Common Fixed Point Theorem for Suzuki Type Contractions via Generalized $Psi$simulation Functions
https://scma.maragheh.ac.ir/article_36368.html
10.22130/scma.2018.78315.359
1
In this paper, a new stratification of mappings, which is called $Psi$simulation functions, is introduced to enhance the study of the Suzuki type weakcontractions. Some wellknown results in weakcontractions 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.
0

129
148


Gholamreza
Heidary Joonaghany
Department of Mathematics, Faculty of Science, Science and Research Branch, Islamic Azad University, Tehran, Iran.
Iran


Ali
Farajzadeh
Department of Mathematics, Faculty of Science, Razi University, Kermanshah 67149, Iran.
Iran
farajzadehali@gmail.com


Mahdi
Azhini
Department of Mathematics, Faculty of Science, Science and Research Branch, Islamic Azad University, Tehran, Iran.
Iran
mahdi.azhini@gmail.com


Farshid
Khojasteh
Department of Mathematics, Faculty of Science, Arak Branch, Islamic Azad University, Arak, Iran.
Iran
fkhojaste@iauarak.ac.ir
Common fixed point
Suzuki type contractions
Generalized $Psi$simulation functions
[[1] Ya.I. Alber and S. GuerreDelabriere, 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. 722.##[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. 10821094.##[3] A.D. Arvanitakis, A proof of the generalized Banach contraction conjecture, Proc. Amer. Math. Soc., 131 (2003), pp. 3647–3656.##[4] S. Banach, Sur les operations dans les ensembles abstraits et leurs applications aux equations integrales, Fund. Math., 3 (1922), pp. 133181.##[5] V. Berinde, Approximating fixed points of weak $varphi$contractions, Fixed Point Theory, 4 (2003), pp. 131142.##[6] D. Doric, Common fixed point for generalized $(psi  varphi)$weak contraction, Appl. Math. Lett., 22 (2009), pp. 18961900.##[7] D. Doric, Z. Kadelburg, and S. Radenovic, EdelsteinSuzukitype fixed point results in metric and abstract metric spaces, Nonlinear Anal., 75 (2012), pp. 19271932.##[8] D. Doric and R. Lazovic, Some Suzukitype fixed point theorems for generalized multivalued mappings and applications, Fixed Point Theory Appl., 2011 (2011), 13 pages.##[9] P.N. Dutta and B.S. Choudhary, A generalization of contraction principle in metric spaces, Fixed Point Theory Appl., 2008 (2008), 8 pages.##[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. 11891194.##[11] M. Kikkawa and T. Suzuki, Some notes on fixed point theorems with constants, Bull. Kyushu Inst. Technol. Pure Appl. Math., 56 (2009), pp. 1118.##[12] M. Kikkawa and T. Suzuki, Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal., 69 (2008), pp. 29422949.##[13] W. Kirk and B. Sims, Handbook of metric fixed point theory, Springer Science & Business Media., 2001.##[14] A. Meir and E. Keeler, A theorem on contraction mappings, J. Math. Anal. Appl., 28 (1969), pp. 326329.##[15] A. Nastasi and P. Vetro, Fixed point results on metric and partial metrric spaces via simulations functions, J. Nonlinear Sci. Appl.,##8 (2015), pp. 10591069.##[16] M. Olgun, O. Bicer, and T. Alyildiz, A new aspect to Picard operators with simulation functions, Turk. J. Math., 40 (2016), pp. 832837.##[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.##[18] B.E. Rhodes, Some theorems on weakly contractive maps, Nonlinear Anal., 47 (2001), pp. 26832693.##[19] A. Roldan, E. Karapinar, C. Roldan, and J. MartinezMoreno, Coincidence point theorems on metric spaces via simulation functions, J. Comput. Appl. Math., 275 (2015), pp. 345–355.##[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] S.L. Singh, R. Kamal, M. De La Sen, and Renu Chugh, A Fixed Point Theorem for Generalized Weak Contractions, Filomat, 29 (2015), pp. 14811490.##[22] S.L. Singh, Renu Chugh, and Raj Kamal, Suzuki type common fixed point theorems and applications, Fixed Point Theory, 14 (2) (2013), pp. 497506.##[23] T. Suzuki, A generalized Banach contraction principle that Characterizes metric completeness, Proc. Amer. Math. Soc., 136 (2008), pp. 18611869.##[24] T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 (11) (2009), pp. 53135317.##[25] Q. Zhang and Y. Song, Fixed point theory for generalized $(psi  varphi)$weak contractions, Appl. Math. Lett., 22 (2009), pp. 7578.##]
1

Coefficient Bounds for Analytic biBazileviv{c} Functions Related to Shelllike Curves Connected with Fibonacci Numbers
https://scma.maragheh.ac.ir/article_36054.html
10.22130/scma.2018.82266.401
1
In this paper, we define and investigate a new class of biBazilevic functions related to shelllike curves connected with Fibonacci numbers. Furthermore, we find estimates of first two coefficients of functions belonging to this class. Also, we give the FeketeSzegoinequality for this function class.
0

149
160


Hatun Ozlem
Guney
Dicle University, Department of Mathematics, Science Faculty, TR21280 Diyarbakir, Turkey.
Iran
ozlemg@dicle.edu.tr
BiBazilevic function
Analytic function
Shelllike curve
Fibonacci numbers
[[1] I.E. Bazilevic, On a case of integrability in quadratures of the LownerKufarev equation, Math. Sb., 37(1955), pp. 471476.##[2] D.A. Brannan, J. Clunie, and W.E. Kirwan, Coefficient estimates for a class of starlike functions, Canad. J. Math., 22 (1970), pp. 476485.##[3] D.A. Brannan and T.S.Taha, On some classes of biunivalent functions, Stud. Univ.BabesBolyai Math., 31 (1986), pp. 7077.##[4] P.L. Duren, Univalent Functions, In: Grundlehren der Mathematischen Wissenschaften, Band 259, New York, Berlin, Heidelberg and Tokyo, SpringerVerlag, 1983.##[5] J. Dziok, R.K. Raina, and J. Sokol, On a class of starlike functions related to a shelllike curve connected with Fibonacci numbers, Math. and Computer Modelling, 57 (2013), pp. 12031211.##[6] J. Dziok, R.K. Raina, and J. Sokol, On $alpha$convex functions related to a shelllike curve connected with Fibonacci numbers, Appl. Math. Comp., 218 (2011), pp. 9961002.##[7] M. Fekete and G. Szego, Eine Bemerkunguber ungerade schlichte Functionen, J. London Math. Soc., 8 (1933), pp. 8589.##[8] M. Lewin, On a coefficient problem for biunivalent functions, Proc. Amer. Math. Soc., 18 (1967), pp. 6368.##[9] X.F. Li and A.P. Wang, Two new subclasses of biunivalent functions, International Mathematical Forum, 7 (2012), pp. 14951504.##[10] Ch. Pommerenke, Univalent Functions, Math. Math, Lehrbucher, Vandenhoeck and Ruprecht, Gottingen, 1975.##[11] R.K. Raina and J. Sokol, FeketeSzego problem for some starlike functions related to shelllike curves, Math. Slovaca, 66 (2016), pp. 135140.##[12] J. Sokol, On starlike functions connected with Fibonacci numbers, Folia Scient. Univ. Tech. Resoviensis, 175 (1999), pp. 111116.##[13] H.M. Srivastava and D. Bansal, Coefficient estimates for a subclass of analytic and biunivalent functions, J. Egyptian Math. Soc., 23 (2015), pp. 242246.##[14] H.M. Srivastava, S. Bulut, M. Caglar, and N. Yagmur, Coefficient estimates for a general subclass of analytic and biunivalent functions, Filomat, 27 (2013), pp. 831842.##[15] H.M. Srivastava, S. Gaboury, and F. Ghanim, Coefficient estimates for some general subclasses of analytic and biunivalent functions, Afr. Mat., 28(2017), pp. 693706.##[16] H.M. Srivastava, S. Gaboury, and F. Ghanim, Initial coefficient estimates for some subclasses of mfold symmetric biunivalent functions, Acta Math. Sci. Ser. B Engl. Ed., 36(2016), pp. 863871.##[17] H.M. Srivastava, S. Gaboury, and F. Ghanim, Coefficient estimates for some subclasses of mfold symmetric biunivalent functions, Acta Univ. Apulensis Math. Inform., 23(2015), pp. 153164.##[18] H.M. Srivastava, A.K. Mishra, and P. Gochhayat, Certain subclasses of analytic and biunivalent functions, Appl. Math. Lett., 23 (2010), pp. 11881192.##[19] Srivastava, S. Sivasubramanian, and R. Sivakumar, Initial coefficient bounds for a subclass of mfold symmetric biunivalent functions, Tbilisi Math. J., 7(2014), pp. 110.##[20] H.M. Srivastava, S. Sumer Eker, and M. Ali Rosihan, Coefficient bounds for a certain class of analytic and biunivalent functions, Filomat, 29(2015), pp. 18391845.##[21] H. Tang, H.M. Srivastava, S. Sivasubramanian, and P. Gurusamy, The FeketeSzego functional problems for some subclasses of mfold symmetric biunivalent functions, J. Math. Inequal., 10 (2016), pp. 10631092.##[22] QH Xu, YC Gui, and H.M. Srivastava, Coefficinet estimates for a certain subclass of analytic and biunivalent functions, Appl. Math. Lett., 25 (2012), pp. 990994.##[23] P. Zaprawa, On the FeketeSzego problem for classes of biunivalent functions, Bull. Belg. Math. Soc. Simon Stevin, 21(2014), pp.169178.##]