Investigating New Subclasses of Bi-Univalent Functions Associated with q-Pascal Distribution Series Using the Subordination Principle

Abstract

In the real world, there are many applications that find the Pascal distribution to be a useful and relevant model. One of these is the normal distribution. In this work, we develop a new subclass of analytic bi-univalent functions by making use of the q-Pascal distribution series as a construction. These functions involve the q-Gegenbauer polynomials, and we use them to establish our new subclass. Moreover, we solve the Fekete–Szegö functional problem and analyze various different estimates of the Maclaurin coefficients for functions that belong to the new subclass.

A Class of Bi-Univalent Functions in a Leaf-Like Domain Defined through Subordination via q̧-Calculus

“…Recently, Srivastava provided a comprehensive survey that explains the mathematical foundations and practical applications of q ¸-derivative operators, within the context of geometric function theory [15]. For those interested in delving deeper into q ¸-calculus and its implications in this field, an abundance of research is at one's disposal, starting with classical publications [16,17], continuing with studies like [18][19][20] and considering very recent research outcome on the topic like [21][22][23][24][25][26][27][28].…”

A Bi-Starlike Class in a Leaf-like Domain Defined through Subordination via q̧-Calculus

“…Recently, Srivastava provided a comprehensive survey that explains the mathematical foundations and practical applications of fractional q ¸-derivative operators, within the context of geometric function theory [17]. For those interested in delving deeper into q ¸-calculus and its implications in this field, an abundance of research is at one's disposal, starting with classical publications [18,19], continuing with studies like [20][21][22][23], and considering very recent research outcomes on the topic like [24][25][26][27][28][29][30][31][32].…”

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]).…”