Convolution features of univalent meromorphic functions generated by Barnes-Mittag-Leffler function

TL;DR

This paper investigates the convolution properties and geometric characteristics of Barnes-Mittag-Leffler functions, a generalization of the Mittag-Leffler function, highlighting their significance in geometric function theory.

Contribution

It establishes new conditions for convolution properties and geometric features of Barnes-Mittag-Leffler functions, expanding understanding in this area.

Findings

Derived new convolution conditions for Barnes-Mittag-Leffler functions.

Established criteria for geometric properties and class membership.

Presented illustrative consequences and corollaries.

Abstract

The Mittag-Leffler function plays an important role in Geometric Function Theory, particularly in the study of analytic and meromorphic function classes. Among its various generalizations, the Barnes-Mittag-Leffler function stands out due to its intricate structure and applications in diverse mathematical fields. In this paper, our main focus is to investigate the convolution properties of these functions and establish conditions that ensure specific geometric characteristics. Additionally, we explore membership relations for functions in these classes. The results obtained in this work are novel, and their significance is demonstrated through various illustrative consequences and corollaries, emphasizing their potential impact in function theory and its applications.