A New Category of Analytical Functions Constructed with Mittag-Leffler Function and Lambert Series

Abstract

This investigation explores a novel subclass of analytical functions, designated as T_J(ξ , ρ, A, B), constructed through the application of a linear operator incorporating both the Mittag-Leffler function and Lambert series. We provide sufficient conditions for an analytic function to be a member of the introduced class, we obtain the distortion theorems, the extreme points and the coefficient bounds. When applicable, additional findings are derived utilizing the established Robin's inequalities that assert upper bounds of the Lambert series coefficients.