Exploiting the Pascal Distribution Series and Gegenbauer Polynomials to Construct and Study a New Subclass of Analytic Bi-Univalent Functions

Abstract

In the present analysis, we aim to construct a new subclass of analytic bi-univalent functions defined on symmetric domain by means of the Pascal distribution series and Gegenbauer polynomials. Thereafter, we provide estimates of Taylor–Maclaurin coefficients a2 and a3 for functions in the aforementioned class, and next, we solve the Fekete–Szegö functional problem. Moreover, some interesting findings for new subclasses of analytic bi-univalent functions will emerge by reducing the parameters in our main results.

The Miller-Ross Poisson distribution and its applications to certain classes of bi-univalent functions related to Horadam polynomials

“…Over the past few years, a significant number of academics have been looking at the bi-univalent functions that are correlated with orthogonal polynomials. Just a few of these functions are [14] , [15] , [16] , [17] , [18] , [19] , [20] , [21] , [22] , [23] , [24] , to name a few more.…”

Classes of Harmonic Functions Related to Mittag-Leffler Function

“…∪ {0}. Inclusion relations between different subclasses of analytic and univalent functions by using hypergeometric functions [10,31], generalized Bessel function [32][33][34] and by the recent investigations related with distribution series [35][36][37][38][39][40][41], were studied in the literature. Very recently, several authors have investigated mapping properties and inclusion results for the families of harmonic univalent functions, including various linear and nonlinear operators (see [42][43][44][45][46][47][48]).…”

An Application of Pascal Distribution Series on Certain Analytic Functions Associated with Stirling Numbers and Sălăgean Operator

“…In recent years, many researchers have examined some important features in the geometric function theory, such as coefficient estimates, inclusion relations, and conditions of being in some known classes, using different probability distributions such as the Poisson, Pascal, Borel, Mittag-Leffler-type Poisson distribution, etc. (see, for example, [6][7][8][9][10]).…”