The Univalency of analytic functions involving a Linear Operator defined by the Mittag-Leffler function and the Lambert series

Abstract

This study introduces a novel linear operator incorporating both the Mittag-Leffler function and Lambert series to establish a new subclass of analytic functions denoted as . We first obtain sufficient conditions for functions to be members of . Consequently, we examine key properties including extreme points, coefficient constraints, and the radii of Univalency and starlikeness for functions in this subclass. In addition, by the means of Robin's inequalities, we provide some coefficients' lower bounds when applicable.