International Journal of Nonlinear Analysis and Applications

Fekete-Szegö problem for two new subclasses of bi-univalent functions defined by Bernoulli polynomial

Document Type : Research Paper

Authors

Karamanoglu Mehmetbey University, Kamıl Ozdag Science Faculty, Department of Mathematics, Karaman, Turkiye

Abstract

This investigation deals with two new subclasses of analytic and bi-univalent functions defined by Bernoulli polynomial. In this paper, coefficient estimation and Fekete-Szegö problems are solved for these newly defined function subclasses. In addition, certain remarks are indicated for the subclasses of bi-starlike and bi-convex functions.

Keywords

[1] I. Aktas and N. Yılmaz, Initial coefficients estimate and Fekete-Szego problems for two new subclasses of biunivalent functions, Konuralp J. Math. 10 (2022), no. 1, 138–148.
[2] T. Al-Hawary, A. Amourah, and B.A. Frasin, Fekete–Szego inequality for bi-univalent functions by means of Horadam polynomials, Bol. Soc. Mat. Mex. 27 (2021), 1–12.
[3] A. Amourah, B.A. Frasin, and T. Abdeljawad, Fekete–Szego inequality for analytic and bi-univalent functions subordinate to Gegenbauer polynomials, J. Funct. Spaces 2021 (2021), 5574673.
[4] A. Amourah, B.A. Frasin, M. Ahmad, and F. Yousef, Exploiting the Pascal distribution series and Gegenbauer polynomials to construct and study a new subclass of analytic bi-univalent functions, Symmetry 14 (2022), no. 1, 147.
[5] D.A. Brannan and T.S. Taha On some classes of bi-univalent function, Stud.Univ. Babes-Bolyai Math. 31 (1986), 70–77.
[6] M. Buyankara and M. Caglar, On Fekete-Szego problem for a new subclass of bi-univalent functions defined by Bernoulli polynomials, Acta Univ. Apulensis Math. Inform. 71 (2022) 137–145.
[7] M. Buyankara, M. Caglar and LI. Cotırla, New subclasses of bi-univalent functions with respect to the symmetric points defined by Bernoulli polynomials, Axioms 11 (2022), 652.
[8] L.I. Cotırla, New classes of analytic and bi-univalent functions, AIMS Math. 6 (2021), 10642–0651.
[9] P.L. Duren, Univalent Functions, Springer Science and Business Media, 2001.
[10] J. Dziok, A general solution of the Fekete-Szego problem, Bound. Value Probl. 2013 (2013), no. 1, 1–13.
[11] M. Fekete and G. Szego Eine bemerkung uber ungerade schlichte funktionen, J. Lond. Math. Soc. 1 (1933), no. 2, 85–89.
[12] B.A. Frasin and M.K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett. 24 (2011), 1569–1573.
[13] H.O. Guney, G. Murugusundaramoorthy, and J. Soko l, Subclasses of bi-univalent functions related to shell-like curves connected with Fibonacci numbers, Acta Univ. Sapientiae Math. 10 (2018), no. 1, 70–84.
[14] M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc. 18 (1967), 63–68.
[15] S.S. Miller and P.T. Mocanu, Differential Subordinations, Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, 2000.
[16] P. Natalini and A. Bernardini, A generalization of the Bernoulli polynomials, J. Appl. Math. 2003 (2003), no. 3, 155–163.
[17] H. Orhan, I. Aktas, and H. Arıkan, On new subclasses of bi-univalent functions associated with the (p, q)-Lucas polynomials and bi-Bazilevic type functions of order ρ + ξ, Turk. J. Math. 47 (2023), no. 1, 98–109.
[18] GI. Oros and LI. Cotırla, Coefficient estimates and the Fekete–Szego problem for new classes of m-fold symmetric bi-univalent functions, Mathematics 10 (2022), 129.
[19] H.M. Srivastava, S. Altınkaya, and S. Yalcın, Certain Subclasses of bi-univalent functions associated with the Horadam polynomials, Iran. J. Sci. Technol. Trans. A Sci. 43 (2019), 1873–1879.
[20] H.M. Srivastava, S. Gaboury, and F. Ghanim, Coefficient estimates for some general subclasses of analytic and bi-univalent functions, Afr. Mat. 28 (2017), 693–706.
[21] H.M. Srivastava, A.K. Mishra, and P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23 (2010), 1188–1192.
[22] H.M. Srivastava, G. Murugusundaramoorthy, and K. Vijaya, Coefficient estimates for some families of bi-Bazilevic functions of the Ma-Minda type involving the Hohlov operator, J. Class. Anal. 2 (2013), no. 2, 167–181.
[23] A.K. Wanas and L.I. Cotırla, Initial coefficient estimates and Fekete–Szego inequalities for new families of biunivalent functions governed by (p − q) Wanas operator, Symmetry 13 (2021), no. 11, 2118.
[24] A.K.Wanas and L.I. Cotırla, New applications of Gegenbauer polynomials on a new family of bi-Bazilevic functions governed by the q-Srivastava-Attiya Operator, Mathematics 10 (2022), no. 8, 1309.
[25] N. Yılmaz and I. Aktas, On some new subclasses of bi-univalent functions defined by generalized bivariate Fibonacci-polynomial, Afr. Mat. 33 (2022), no. 2, 59.
[26] P. Zaprawa, On the Fekete-Szego problem for classes of bi-univalent functions, Bull. Belg. Math. Soc. Simon Stevin 21 (2014), no. 1, 169–178.
International Journal of Nonlinear Analysis and Applications
Volume 15, Issue 10
October 2024
Pages 1-10
  • Receive Date: 06 March 2023
  • Accept Date: 19 October 2023