On the Fekete-Szego problem associated with generalized fractional operator

Document Type : Research Paper

Authors

Department of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600, Bangi, Selangor, Malaysia

Abstract

In this paper, the classical Fekete-Szego problem is studied regarding a class of univalent functions generated using a generalized fractional differential operator. The results presented in the main theorem are new generalizations for well-known results.

Keywords

[1] A. Chonweerayoot, D.K. Thomas and W. Upakarnitikaset, On the coefficient of close-to-convex functions, Math. Japon., 36 (1991), 819–826.
[2] L.I. Cotˆırl˜a, New classes of analytic and bi-univalent functions, AIMS Math. 6 (2021), no. 10, 10642–10651.
[3] M. Darus and D.K. Thomas, On the Fekete-Szeg¨o problem for close-to-convex functions, Math. Japon. 47 (1998), 125–132.
[4] M. Darus, On the coefficient problem with Hadamard product, J. Anal. Appl. 2 (2004), 87–93.
[5] M. Fekete and G. Szeg¨o, Eine Bemerkung ¨uber undrade schlicht Funktionen, J. London Math. Soc. 8 (1933), 85–89.
[6] B. Frasin and M. Darus, On the Fekete-Szeg¨o problem using Hadamard product, Int. Math. J. 3 (2003), 1289–1296.
[7] O. Halit and L.I. Cotˆırl˜a, Fekete-Szeg¨o inequalities for some certain subclass of analytic functions defined with Ruscheweyh derivative operator, Axioms 11 (2022), no. 10, 560.
[8] A. Issa and M. Darus, Fekete-Szeg¨o problem of strongly -close-toconvex functions associated with generalized fractional operator, Georg. Math. J. 2022. Accepted. https://doi.org/10.1515/gmj-2022-2197.
[9] A. Issa and M. Darus, Generalized complex fractional derivative and integral operators for the unified class of analytic functions, Int. J. Math. Comput. Sci. 15 (2020), no. 3, 857–868.
[10] A. Issa and M. Darus, Application of generalized fractional operatores in subclass of uniformly convex functions, J. Math. Anal. 13 (2022), no. 5, 21–34.
[11] M. Jahangiri, A coefficient inequality for a class of close-to-convex functions, Math. Japon. 41 (1995), no. 3, 557–559.
[12] W. Kaplan, Close-to-convex schlicht functions, Mich. Math. J. 1 (1952), 169–185.
[13] K.R. Karthikeyan and G. Murugusundaramoorthy, Unified solution of initial coefficients and Fekete–Szeg¨o problem for subclasses of analytic functions related to a conic region, Afr. Mat. 33 (2022), no. 2, 1–12.
[14] R.R. London, Fekete-Szeg¨o problem for close-to-convex functions, Amer. Math. Soc. 117 (1993), 947–950.
[15] C.H. Pommerenke, Univalent Functions, Vandenhoek and Ruprecht, G¨ottingen, 1975.
[16] H.M. Srivastava, T.G. Shaba, G. Murugusundaramoorthy, A.K. Wanas and G.I. Oros, The Fekete-Szeg¨o functional and the Hankel determinant for a certain class of analytic functions involving the Hohlov operator, AIMS Math. 8 (2023), no. 1, 340–360.
[17] S.R. Swamy and S. Altınkaya, Fekete-Szeg¨o functional for regular functions based on quasi-subordination, Int. J. Nonlinear Anal. Appl. 13 (2022), no. 2, 1105–1115.
Volume 14, Issue 1
January 2023
Pages 25-32
  • Receive Date: 18 August 2022
  • Revise Date: 09 November 2022
  • Accept Date: 09 December 2022