Studying the Harmonic Functions Associated with Quantum Calculus

Abstract

Using the derivative operators’ q-analogs values, a wide variety of holomorphic function subclasses, q-starlike, and q-convex functions have been researched and examined. With the aid of fundamental ideas from the theory of q-calculus operators, we describe new q-operators of harmonic function Hϱ,χ;qγF(ϖ) in this work. We also define a new harmonic function subclass related to the Janowski and q-analog of Le Roy-type functions Mittag–Leffler functions. Several important properties are assigned to the new class, including necessary and sufficient conditions, the covering Theorem, extreme points, distortion bounds, convolution, and convex combinations. Furthermore, we emphasize several established remarks for confirming our primary findings presented in this study, as well as some applications of this study in the form of specific outcomes and corollaries.

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].…”

New Subfamily of Bi-starlike and Bi-convex Functions Defined by the q-Janowski Function

“…This article presents an overview of q-calculus, initially introduced by Jackson and subsequently explored by numerous mathematicians [17][18][19][20][21][22][23]. It focuses on introducing key concepts and definitions within the realm of q-calculus.…”