GENERALISED SUBCLASSES OF ANALYTIC FUNCTIONS WITH VARYING ARGUMENTS ASSOCIATED WITH q-DIFFERENCE OPERATOR

In this paper we introduce new subclasses V Eq(n, A, B, λ, α, β, ξ) and V Gq(n, A, B, λ, α, β, ξ) of analytic functions with varying arguments defined by using difference operator in U.This operator, which generalizes the classical difference operator, plays a pivotal role in the study of various mathematical structures. The research work explores the properties and characteristics of these subclasses within the realm of analytic functions with varying arguments. It delves into the behavior and analytical properties of functions belonging to these subclasses, shedding light on Coefficient estimates, distortion theorems and extreme points. Additionally, the paper likely discusses the interplay between the q-difference operator and the varying arguments, elucidating how these elements influence the structure and behavior of the analytic functions under consideration. By elucidating the properties and behaviors of these generalized subclasses, the research work aims to contribute to the broader understanding of analytic functions within the framework of q-calculus and related mathematical areas. This investigation may have implications for various mathematical disciplines, including complex analysis, functional analysis, and mathematical physics.