CERTAIN CLASS OF ANALYTIC AND UNIVALENT FUNCTION WITH RESPECT TO SYMMETRIC

Abstract

This study delves into the intricate properties of analytic functions within the unit disk, specically focusing on classes s*(α, β, ξ, γ) and K*(α, β, ξ, γ) characterized by symmetric properties with negative coecients. We present the ndings on key aspects such as coecient inequalities establishing bounds on the coecients of functions belonging to the classes. Also, determine the convexity radius for functions in a class and distortion theorems. Distortion theorems will be presented to provide bounds within the unit disk. These bounds are critical for understanding the behavior and geometric properties of these functions. Symmetric Classes with Negative Coecients: Classes are dened by their symmetry and negative coecients. Functions in these classes exhibit specic geometric properties that are crucial for applications in complex analysis.