Geometric Attributes of Analytic Functions Generated by Mittag-Leffler Function

This study examines the necessary requirements for some analytic function subclasses, especially those associated with the generalized Mittag-Leffler function, to be classified as univalent function subclasses that are determined by particular geometric constraints. The core methodology revolves around the application of the Hadamard (or convolution) product involving a normalized Mittag-Leffler function Mκ,χ(ζ), leading to the definition of a new linear operator Sχ,ϑκℏ(ζ). We investigate inclusion results in the recently defined subclasses Ξ˜(ϖ,ϱ),L^(ϖ,ϱ),K^(ϖ,ϱ) and F^(ϖ,ϱ), which generalize the classical classes of starlike, convex, and close-to-convex functions. This is achieved by utilizing recent developments in the theory of univalent functions. In addition, we examine the behavior of functions from the class Rθ(E,V) under the action of the convolution operator Wχ,ϑκh(ζ), establishing sufficient criteria for the resulting images to lie within the subclasses of analytic function. Also, certain mapping properties related to these subclasses are analyzed. In addition, the geometric features of an integral operator connected to the Mittag-Leffler function are examined. A few particular cases of our main findings are also mentioned and examined and the paper ends with the conclusions regarding the obtained results.