Initial bounds for analytic and bi-univalent functions by means of (p,q)−Chebyshev polynomials defined by differential operator

Abstract

In this paper, a subclass T ζ Σ (m, γ, λ, p, q) of analytic and bi-univalent functions by means of (p, q)−Chebyshev polynomials is introduced. Certain coefficient bounds for functions belong to this subclass are obtained. In addition, the Fekete-Szegö problem is solved in this subclass.

Fekete-Szegö Inequality for Analytic and Biunivalent Functions Subordinate to Gegenbauer Polynomials

“…Recently, many researchers have been exploring biunivalent functions associated with orthogonal polynomials, few to mention [22][23][24][25][26][27][28]. For Gegenbauer polynomial, as far as we know, there is little work associated with biunivalent functions in the literatures.…”

Coefficient Bounds and Fekete-Szeg¨o inequality for a Certain Families of Bi-Prestarlike Functions Defined by (M,N)-Lucas Polynomials

“…A function U ∈ A is said to be bi-univalent in O if both U and U −1 are univalent in O, let we name by the notation E the set of bi-univalent functions in O satisfying (1.1). In fact, Srivastava et al [32] refreshed the study of holomorphic and biunivalent functions in recent years, it was followed by other works as those by Frasin and Aouf [15], Altinkaya and Yalçin Journal of Advances in Mathematics Vol 20 (2021) ISSN: 2347-1921 https://rajpub.com/index.php/jam [5], Güney et al [16] and others (see, for example [1,3,8,10,11,18,21,22,23,26,27,28,29,30,31,33,34,35,38,39,41]).…”