Faber polynomial coefficient estimates for a class of analytic bi-univalent functions

Abstract

In the present paper, we were mainly concerned with obtaining estimates for the general Taylor-Maclaurin coefficients for functions in a certain general subclass of analytic bi-univalent functions. For this purpose, we used the Faber polynomial expansions. Several connections to some of the earlier known results are also pointed out.2010 Mathematics Subject Classification. 30C45.

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

“…A function f ∈ A is said to be in Σ the class of bi-univalent in U if both f (z) and f −1 (z) are univalent in U. Lewin [9] showed that |a 2 | < 1.51 for every function f ∈ Σ given by (1.1). Posteriorly, Brannan and Clunie [3] improved Lewin's result and conjectured that |a 2 | ≤ √ 2 for every function f ∈ Σ given by (1.1). The coefficient estimate problem for each of the following Taylor Maclaurin coefficients:…”

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.…”

Certain subclasses of Pseudo-type meromorphic bi-univalent functions

“…Recently, Some several researcher such as ( for example [1], [2], [3], [4] [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [17], [21]) introduced new subclasses of bi-univalent functions and meromorphically bi-univalent functions and obtained estimates on the initial coefficients for functions in each of these subclasses.…”