Open AccessNew Families of Bi-Univalent Functions Governed by Gegenbauer Polynomials
Author(s) -
Abbas Kareem Wanas
Publication year - 2021
Publication title -
earthline journal of mathematical sciences
Language(s) - English
Resource type - Journals
ISSN - 2581-8147
DOI - 10.34198/ejms.7221.403427
Subject(s) - holomorphic function , sigma , mathematics , pure mathematics , gegenbauer polynomials , orthogonal polynomials , combinatorics , algebra over a field , classical orthogonal polynomials , physics , quantum mechanics
The aim of this article is to initiating an exploration of the properties of bi-univalent functions related to Gegenbauer polynomials. To do so, we introduce a new families \mathbb{T}_\Sigma (\gamma, \phi, \mu, \eta, \theta, \gimel, t, \delta) and \mathbb{S}_\Sigma (\sigma, \eta, \theta, \gimel, t, \delta ) of holomorphic and bi-univalent functions. We derive estimates on the initial coefficients and solve the Fekete-Szeg problem of functions in these families.