Defining and Analyzing New Classes Associated with (<i>λ</i>,<i>γ</i>)-Symmetrical Functions and Quantum Calculus

Abstract

In this paper, we introduce new classes of functions defined within the open unit disk by integrating the concepts of (λ,γ)-symmetrical functions, generalized Janowski functions, and quantum calculus. We derive a structural formula and a representation theorem for the class Sqλ,γ(x,y,z). Utilizing convolution techniques and quantum calculus, we investigate convolution conditions supported by examples and corollary, establishing sufficient conditions. Additionally, we derive properties related to coefficient estimates, which further elucidate the characteristics of the defined function classes.

Keywords

• convolution
• Janowski functions
• <i>q</i>-calculus
• (<i>λ</i>,<i>γ</i>)-symmetric points