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  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  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  O.A. Boikanyo and G. Morosanu, A contraction proximal point algorithm with two monotone operators, Nonlinear Anal. (TMA), 75 (2012), pp. 5686-5692. 3  O.A. Boikanyo and G. Morosanu, On the method of alternating resolvents, Nonlinear Anal. (TMA), 74 (2011), pp. 5147-5160. 4  O.A. Boikanyo and G. Morosanu, Strong convergence of the method of alternating resolvents, J. Nonlinear Convex Anal., 14 (2013), pp. 221-229. 5  O.A. Boikanyo and G. Morosanu, The method of alternating resolvents revisited, Numer. Funct. Anal. Optim., 33 (2012), pp. 1280-1287. 6  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  K. Goebel and S. Reich, Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings, Marcel Dekker, New York and Basel, 1984. 8  H. Hundal, An alternating projection that does not converge in norm, Nonlinear Anal. (TMA), 57 (2004), pp. 35-61. 9  E. Kopecka and S. Reich, A note on the von Neumann alternating projections algorithm, J. Nonlinear Convex Anal., 5 (2004), pp. 379-386. 10  P.E. Mainge, Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization, Set-Valued Anal., 16 (2008), pp. 899-912. 11  E. Matouskova and S. Reich, The Hundal example revisited, J. Nonlinear Convex Anal., 4 (2003), pp. 411-427. 12  G. Morosanu, Nonlinear Evolution Equations and Applications, Reidel, Dordrecht, 1988. 13  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  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  H.K. Xu, A regularization method for the proximal point algorithm, J. Glob. Optim., 36 (2006), pp. 115-125. 16  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  T. Bag and S.K. Samanta, Finite dimensional fuzzy normed linear spaces, J. Fuzzy Math., 11 (2003), pp. 687-705. 1  T. Bag and S.K. Samanta, Fuzzy bounded linear operators, Fuzzy Sets and Systems, 151 (2005), pp. 513-547. 2  T. Bag and S.K. Samanta, Some fixed point theorems in fuzzy normed linear spaces, Inf. Sci., 177 (2007), pp. 3271-3289. 3  M. Berinde, Approximate fixed point theorems, Mathematica, LI (1) (2006). 4  V. Berinde, Approximating fixed points of weak contractions using the Picard iteration, Nonlinear Anal. Forum, 9 (2004). 5  V. Berinde, On the approximation of fixed points of weak contractive mappings, Math., 19 (2003), pp. 7-22. 6  S.K. Chatterjea, Fixed-point theorems, C.R. Acad. Bulgare Sci. 25 (1972), pp. 727-730. 7  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  A. Chitra and P.Y. Mordeson, Fuzzy linear operators and fuzzy normed linear spaces, Bull. Calcutta Math. Soc., 74 (1969), pp. 660-665. 9  Lj. B. Ciric, A generalization of Banach’s contraction principle, Proc. Am. Math. Soc., 45 (1974), pp. 267-273. 10  C. Felbin, Finite dimensional fuzzy normeded linear spaces, Fuzzy Sets and Systems, 48 (1992), pp. 239-248. 11  O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy Sets and Systems, 12 (1984), pp. 215-229. 12  R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc., 10 (1968), pp. 71-76. 13  A.K. Katsaras, Fuzzy topological vector spaces II, Fuzzy Sets and Systems, 12 (1984), pp. 143-154. 14  I. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica, 11 (1975), pp. 326-334. 15  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  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  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  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 . 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  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  I. Beg and A.R. Butt, Fixed point of set-valued graph contractive mappings, J. Inequa. Appl., (2013), 2013:252. 2  M. Edelstein, An extension of Banach's contraction principle, Proc. Amer. Math. Soc., 12 (1961), pp. 7-10. 3  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  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  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  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  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  N. Mehmood, A. Azam, and S. Aleksic, Topological vector-space valued cone Banach spaces, Int. J. Anal. Appl., 6 (2014), pp. 205-219. 9  M. Ramezani, Orthogonal metric space and convex contractions, Int. J. Nonlinear Anal. Appl., 6 (2015), pp. 127-132. 10  M. Ramezani, H. Baghani, Contractive gauge functions in strongly orthogonal metric spaces, Int. J. Nonlinear Anal. Appl., 8 (2017), pp. 23-28. 11  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  O. Christensen, An introduction to Frames and Riesz Bases, Birkhauser, Boston, 2003. 1  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  M. Fatemidokht and A. Askari Hemmat, $P$-adic shearlets, Wavel. Linear Algebra, to appear 3  B. Han, On dual wavelet tight frames, Appl. Comput. Harmon. Anal., 4 (1997), pp. 380-413. 4  G. Kutyniok and D. Labate, Construction of regular and irregular shearlet frames, J. Wavelet Theory Appl., 1 (2007), pp. 1-10. 5  G. Kutyniok and D. Labate, Shearlets: Multiscle Analysis for Multivariate Data, Birkhauser. Basel, 2012. 6  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  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  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  B.G. Bodmann and P.G. Casazza, The road to equal-norm Parseval frames, J. Funct. Anal., 258 (2010), pp. 397-420. 3  J. Cahill, P.G. Casazza, and G. Kutyniok, Operators and frames, J. Operator Theory., 70 (2013), pp. 145-164. 4  P.G. Casazza and J. Kovacevic, Equal-norm tight frames with erasures, Adv. Comput. Math., 18 (2003), pp. 387-430. 5  O. Christensen, An Introduction to Frames and Riesz Bases, Birkhauser., Boston, Basel, Berlin, 2002. 6  O. Christensen and Y. Eldar, Oblique dual frames and shift-invariant spaces, Appl. Comput. Harmon. Anal., 17 (2004), pp. 48-68. 7  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  D. Freeman and D. Speegle, The discretization problem for continuous frames., https://arxiv.org/abs/1611.06469. 9  V.K. Goyal, J. Kovacevic, and J.A. Kelner, Quantized frame expansions with erasures, Appl. Comput. Harmon. Anal., 10 (2001), pp. 203-233. 10  C. Heil, Y.Y. Koo, and J.K. Lim, Duals of frame sequences, Acta Appl. Math., 107 (2008), pp. 75-90. 11  C. Heil and D. Walnut, Continuous and discrete wavelet transform, SIAM Rev., 31 (1969), pp. 628-666. 12  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  S. Li and H. Ogawa, Pseudo duals of frames with applications, Appl. Comput. Harmon. Anal., 11 (2001), pp. 289-304. 14  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  N.I. Ahiezer, Elements of theory of elliptic functions, Moscow, 1970. 1  G.D. Anderson, M.K. Vamanamurthy, and M.K. Vourinen, Conformal invariants, inequalities and quasiconformal maps, Wiley-Interscience, 1997. 2  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  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  P.L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften (Fundamental Principles of Mathematical Science), vol. 259, Springer-Verlag, New York, Berlin, 1983. 5  B.A. Frasin, Coefficient bounds for certain classes of bi-univalent functions, Hacettepe J. Math. Stat., 43 (2014), pp. 383-389. 6  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  S. Kanas and A. Wisniowska, Conic regions and k-uniform convexity, J. Comput. Appl. Math., 105 (1999), pp. 327-336. 8  S. Kanas and A. Wisniowska, Conic domains and starlike functions, Rev. Roumaine Math. Pures Appl., 45 (2000), pp. 647-657. 9  S. Kanas, Coefficient estimates in subclasses of the Caratheodory class related to conical domains, Acta Math. Univ. Comenian., 74 (2005), pp. 149-161. 10  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  N. Khan, Q.Z. Ahmad, T. Khalid, and B. Khan, Results on spirallike $p$-valent functions, AIMS Math., 3 (2018), pp. 12-20. 12  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  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  K.I. Noor, On a generalization of uniformly convex and related functions, Comput. Math. Appl., 61 (2011), pp. 117-125. 15  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  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  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  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  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  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  M. Obradovic and S. Owa, Some sufficient conditions for strongly starlikeness, Int. J. Math. Math. Sci., 24 (2000), pp. 643-647. 22  M. Raza, M. U Din, and S.N. Malik, Certain geometric properties of normalized wright functions, J. Func. Spaces, 2016 (2016), 9 pages. 23  W. Rogosinski, On the coefficients of subordinate functions, Proc. Lond. Math. Soc., 48 (1943), pp. 48-82. 24  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  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  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  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  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  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  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  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  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&quot;, Institute of Mathematics and Mechanics of NAS of Azerbaijan, AZ1141, Baku, Azerbaijan. AUTHOR  D.R. Adams, Morrey spaces, Springer, 2016. 1  B.T. Bilalov, On isomorphisms of two bases in $L_{p}$, Fundam. Prikl. Mat., 1 (1995), pp. 1091-1094. 2  B.T. Bilalov, T.B. Gasymov, and A.A. Guliyeva, On solvability of Riemann boundary value problem in Morrey-Hardy classes, Turkish J. Math., 40 (2016), pp. 1085-1101. 3  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. 4  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. 14-23. 5  B.T. Bilalov and A.A. Quliyeva, On basicity of exponential systems in Morrey-type spaces, Internat. J. Math., 25 (2014), 10 pages. 6  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. 43-48. 7  J.B. Conway, Functions of one complex variable, II, Springer-Verlag, 2012. 8  D.V. Cruz-Uribe and A. Fiorenza, Variable Lebesgue spaces: Foundations and Harmonic Analysis, Springer, 2013. 9  L. Diening, P. Harjulehto, P. Hasto, and M. Ruzicka, Lebesgue and Sobolev spaces with variable exponents, Springer-Verlag, Berlin, 2017. 10  G.M. Goluzin, Geometric theory of functions of complex variables, AMS Trans. Math. Monographes, 29, 1969. 11  D.M. Israfilov and N.P. Tozman, Approximation in Morrey--Smirnov classes, Azerb. J. Math., 1 (2011), pp. 99-113. 12  Y. Katznelson, Sets of uniqueness for some classes of trigonometric series, Bull. Amer. Math. Soc., 70 (1964), 722-723. 13  V. Kokilashvili, A. Meskhi, H. Rafeiro, and S. Samko, Integral Operators in Non-standard function spaces, Birkhauser, 2, 2016. 14  P. Koosis, Introduction to $H_p$ spaces, 2nd edition, CUP, 1998. 15  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  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  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  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  S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fund. Math., 3 (1922), pp. 133-181. 4  Lj.B. Ciric, A generalization of Banach’s contraction principle, Proc. Amer. Math. Soc., 45 (1974), pp. 267-273. 5  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  W.S. Du, Some new results and generalizations in metric fixed point theory, Nonlinear Anal., 73 (2010), pp. 1439-1446. 7  G. Durmaz, G. Mınak, and I. Altun, Fixed points of ordered F-contractions, Hacet. J. Math. Stat., 45 (2016), pp. 15-21. 8  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. 9  J. Matkowski, Fixed point theorems for mappings with a contractive iterate at a point, Proc. Amer. Math. Soc., 62 (1977), pp. 344-348. 10  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 11  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  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  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. 14  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  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  B.E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal., 47 (2001), pp. 2683-2693. 17  A. Tarski, A lattice-theoretical fixpoint theorem and its applications, Pacific J. Math., 5 (1955), pp. 285-309., MR0074376. 18  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  M. Azhini and N. Haddadzadeh, Fusion frames in Hilbert modules over pro-C*-algebras, Int. J. Industrial Math., 5 (2013), pp. 109-118. 1  P.G. Casazza and G. Kutyniok, Frames of subspaces, Contemp. Math., Amer. Math. Soc., 345 (2004), pp. 87-113. 2  I. Daubechies, A. Grossmann, and Y. Meyer, Painless nonorthogonal expansions, J. Math. Phys., 27 (1986), pp. 1271-1283. 3  R.J. Duffin and A.C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc., 72 (1952), pp. 341-366. 4  M. Frank and D.R. Larson, Frames in Hilbert C*-modules and C*-algebras, J. Operator Theory., 48 (2002), pp. 273-314. 5  N. Haddadzadeh, G-frames in Hilbert pro-C*-modules, Int. Electron. J. Pure Appl. Math., 105 (2015), pp. 727-743. 6  M. Joita, Hilbert Modules Over Locally C*-Algebras, University of Bucharest Press, ISBN 973737128-3, 2006. 7  M. Joita, On frames in Hilbert modules over pro-C*-algebras, Topology and its Applications., 156 (2008), pp. 83-92. 8  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  W.L. Paschke, Inner product modules over B*-algebras, Trans. Amer. Math. Soc., 182 (1973), pp. 443-468. 10  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  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  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  S. Fujishige,  Submodular functions and optimization, Elsevier., Amesterdam, 2005. 2  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  M. Gr"otschel, L. Lov'asz, and A. Schrijver,  The ellipsoid method and its consequences in combinatorial optimization, Combinatorica., 1 (1981), pp. 169-197. 4  M. Gr"otschel, L. Lov'asz, and A. Schrijver, Geometric algorithms and combinatorial optimization, Springer-Verlag., Berlin Heidelberg, 2012. 5  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  S. Iwata, L. Fleischer, and S. Fujishige, A combinatorial strongly polynomial algorithm for minimizing submodular functions, J. ACM., 48 (2001), pp. 761-777. 7  S. Jegelka and J. Bilmes,  Cooperative cuts for image segmentation, Technical Report, University of Washington, Seattle,  2010. 8  A. Krause and D. Golovin,  Submodular function maximization, in: Tractability: Practical Approaches to Hard Problems, Cambridge Univ. Press., Cambridge, 2014, 71-104. 9  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  S.T. McCormick,  Submodular function minimization, Handbooks Oper. Res. Management Sci., 12 (2005), pp. 321-391. 11  H. Nagamochi,  Minimum degree orderings, Algorithmica., 56 (2010), pp. 17–34. 12  H. Nagamochi and T. Ibaraki, A note on minimizing submodular functions, Inform. Process. Lett., 67 (1998), pp. 239-344. 13  N. Nisan,  T. Roughgarden, E. Tardos, and  V.V. Vazirani,  Algorithmic game theory, Cambridge Univ. Press., New York, USA, 2007. 14  J.B. Orlin,  A faster strongly polynomial time algorithm for submodular function minimization, Math. Program., 118 (2009), pp. 237-251. 15  M. Queyranne,  Minimizing symmetric submodular functions, Math. Program., 82 (1998), pp. 3-12. 16  A. Schrijver,  A combinatorial algorithm minimizing submodular functions in strongly polynomial time, J. Combin. Theory Ser. B., 80 (2000), pp. 346-355. 17  A. Schrijver, Combinatorial optimization: polyhedra and efficiency, Springer-Verlag., Berlin Heidelberg, 2003. 18  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  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  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  A.D. Arvanitakis, A proof of the generalized Banach contraction conjecture, Proc. Amer. Math. Soc., 131 (2003), pp. 3647–-3656. 3  S. Banach, Sur les operations dans les ensembles abstraits et leurs applications aux equations integrales, Fund. Math., 3 (1922), pp. 133-181. 4  V. Berinde, Approximating fixed points of weak $varphi$-contractions, Fixed Point Theory, 4 (2003), pp. 131-142. 5  D. Doric, Common fixed point for generalized $(psi - varphi)$-weak contraction, Appl. Math. Lett., 22 (2009), pp. 1896-1900. 6  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  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  P.N. Dutta and B.S. Choudhary, A generalization of contraction principle in metric spaces, Fixed Point Theory Appl., 2008 (2008), 8 pages. 9  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. 10  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. 11  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. 12  W. Kirk and B. Sims, Handbook of metric fixed point theory, Springer Science & Business Media., 2001. 13  A. Meir and E. Keeler, A theorem on contraction mappings, J. Math. Anal. Appl., 28 (1969), pp. 326-329. 14  A. Nastasi and P. Vetro, Fixed point results on metric and partial metrric spaces via simulations functions, J. Nonlinear Sci. Appl., 15 8 (2015), pp. 1059-1069. 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. 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. 2683-2693. 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. 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. 1481-1490. 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  T. Suzuki, A generalized Banach contraction principle that Characterizes metric completeness, Proc. Amer. Math. Soc., 136 (2008), pp. 1861-1869. 24  T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 (11) (2009), pp. 5313-5317. 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  I.E. Bazilevic, On a case of integrability in quadratures of the Lowner-Kufarev equation, Math. Sb., 37(1955), pp. 471-476. 1  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. 2  D.A. Brannan and T.S.Taha, On some classes of bi-univalent functions, Stud. Univ.Babes-Bolyai Math., 31 (1986), pp. 70-77. 3  P.L. Duren, Univalent Functions, In: Grundlehren der Mathematischen Wissenschaften, Band 259, New York, Berlin, Heidelberg and Tokyo, Springer-Verlag, 1983. 4  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. 5  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. 6  M. Fekete and G. Szego, Eine Bemerkunguber ungerade schlichte Functionen, J. London Math. Soc., 8 (1933), pp. 85-89. 7  M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc., 18 (1967), pp. 63-68. 8  X.F. Li and A.P. Wang, Two new subclasses of bi-univalent functions, International Mathematical Forum, 7 (2012), pp. 1495--1504. 9  Ch. Pommerenke, Univalent Functions, Math. Math, Lehrbucher, Vandenhoeck and Ruprecht, Gottingen, 1975. 10  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. 11  J. Sokol, On starlike functions connected with Fibonacci numbers, Folia Scient. Univ. Tech. Resoviensis, 175 (1999), pp. 111-116. 12  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. 13  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. 14  H.M. Srivastava, S. Gaboury, and F. Ghanim, Coefficient estimates for some general subclasses of analytic and bi-univalent functions, Afr. Mat., 28(2017), pp. 693-706. 15  H.M. Srivastava, S. Gaboury, and F. Ghanim, Initial coefficient estimates for some subclasses of m-fold symmetric bi-univalent functions, Acta Math. Sci. Ser. B Engl. Ed., 36(2016), pp. 863-871. 16  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. 17  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. 18  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. 19  H.M. Srivastava, S. Sumer Eker, and M. Ali Rosihan, Coefficient bounds for a certain class of analytic and bi-univalent functions, Filomat, 29(2015), pp. 1839-1845. 20  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. 21  QH Xu, YC Gui, and H.M. Srivastava, Coefficinet estimates for a certain subclass of analytic and bi-univalent functions, Appl. Math. Lett., 25 (2012), pp. 990-994. 22  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