On Initial Chebyshev Polynomial Coefficient Problem for Certain Subclass of Bi-Univalent Functions

F. Müge Sakar; Ertuğrul Doğan

doi:10.26713/cma.v11i1.1331

Authors

F. Müge Sakar Department of Business Administration, Faculty of Management and Economics, Dicle University, Diyarbakır
Ertuğrul Doğan Master's Degree in Mathematics, Institue of Science, Batman University, Batman

DOI:

https://doi.org/10.26713/cma.v11i1.1331

Keywords:

Initial coefficients problem, Bi-univalent function, Chebyshev polinomials, Fekete-Szegö problem

Abstract

In this paper, we firstly, introduced the subclass \(R_{\Sigma}(\tau ,\alpha ,\gamma ;t)\) satisfying subordinate conditions. Subsequently, considering this defined subclass, initial coefficient estimations are established using by Chebyshev polynomials expansions, and Fekete-Szegö inequalities are also derived for functions belonging to the said subclass. Furthermore, Some relevant consequences of these results are also discussed.

522 310

Downloads

Download data is not yet available.

References

S. Altınkaya and S. Yalçın, Fekete-Szegö inequalities for certain classes of bi-univalent functions, International Scholarly Research Notices 2014 (2014), Article ID 327962, 6 pages, DOI: 10.1155/2014/327962.

S. Aytas, F. M. Sakar and H. í–. Güney, Fekete-Szegö problem for p-valently starlike functions with complex order, ARPN Journal of Science and Technology 5(10) (2015), 514 – 519.

S. Bulut, N. Magesh and V. K. Balaji, Initial bounds for analytic and bi-univalent functions by means of Chebyshev polynomials, Journal of Classical Analysis 11(1) (2017), 83 – 89, DOI: 10.7153/jca-11-06.

E. H. Doha, The first and second kind Chebyshev coefficients of the moments of the general-order derivative of an infinitely differentiable function, International Journal of Computer Mathematics 51 (1994), 21 – 35, DOI: 10.1080/00207169408804263.

J. Dziok, R. K. Raina and J. SokóÅ‚, Application of Chebyshev polynomials to classes of analytic functions, Comptes Rendus Mathematique 353 (2015), 433 – 438, DOI: 10.1016/j.crma.2015.02.001.

M. Fekete and G. Szegö, Eine Bemerkung über ungerade schlichte Funktionen, Journal of the London Mathematical Society s1-8(2) (1933), 85 – 89 (in German), DOI: 10.1112/jlms/s1-8.2.85.

J. C. Mason, Chebyshev polynomial approximations for the L-membrane eigenvalue problem, SIAM Journal on Applied Mathematics 15 (1967), 172 – 186, DOI: 10.1137/0115014.

H. Orhan, N. Magesh and V. K. Balaji, Fekete-Szegö problem for certain classes of Ma-Minda bi-univalent functions, Afrika Matematika 27 (2016), 889 – 897, DOI: 10.1007/s13370-015-0383-y.

F. M. Sakar, S. Aytas and H. í–. Güney, On the Fekete Szegö problem for generalized (M_{alpha,beta}(gamma)) defined by differential operator, Süleyman Demirel íœniversitesi Fen Bilimleri Enstitüsü Dergisi 20(3) (2016), 456 – 459, DOI: 10.19113/sdufbed.12069.

T. Whittaker and G. N. Watson, A Course of Modern Analysis, Cambridge University Press, Cambridge (1996), DOI: 10.1017/CBO9780511608759.

P. Zaprawa, On Fekete-Szegö problem for classes of bi-univalent functions, Bulletin of the Belgian Mathematical Society - Simon Stevin 21 (2014), 169 – 178, DOI: 10.36045/bbms/1394544302.