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

F. Müge Sakar, Ertuğrul Doğan


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.


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

Full Text:



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. Ö. 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. Sokół, 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. Ö. Güney, On the Fekete Szegö problem for generalized (M_{alpha,beta}(gamma)) defined by differential operator, Süleyman Demirel Üniversitesi 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.

DOI: http://dx.doi.org/10.26713%2Fcma.v11i1.1331


  • There are currently no refbacks.

eISSN 0975-8607; pISSN 0976-5905