New Families of Bi-Univalent Functions Governed by Gegenbauer Polynomials | Zendy

Abbas Kareem Wanas | Zendy

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New 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.

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