Abstract
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.
Highlights
“In [20] Legendre studied orthogonal polynomials comprehensively
The Gegenbauer polynomials is special case of orthogonal polynomials. They are representatively related with typically real functions as discovered in [19]
Real functions play an important role in the geometric function theory because of the relation =
Summary
“In [20] Legendre studied orthogonal polynomials comprehensively. The importance of orthogonal polynomials for contemporary mathematics as well as for a wide range of their applications in physics and engineering, is beyond any doubt. Keywords and phrases: holomorphic function, bi-univalent function, Gegenbauer polynomials, Fekete-Szegö problem, coefficient estimates. Let A indicate the family of bi-univalent functions in ) satisfying (1.1).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
