P. Vijayaraju, K. Sethukumarasamy, R. Ambrose Prabhu, and S. Bhaskaran. On Starlikeness and Convexity of Normalized Mittag-Leffler Function with Three Parameters. Dynamic Systems and Applications 30 (2021) No. 7, 1139–1148

https://doi.org/10.46719/dsa20213075

ABSTRACT. 
This article contributes to the investigation of geometric properties of normalized Mittag-Leffler (M-L) function with three parameters in complex plane. We discuss the sufficient conditions required for the normalized three parameter M-L functions to be starlike and convex in the open unit disk. Some interesting relationship between the normalized M-L function with three parameters and hypergeometric functions are given. Also, certain special cases are characterized through mappings over open unit disk.

AMS Subject Classification: 30C45, 33E12, 26A33, 34A08
Keywords: Star Like Function, Convex Function, Mittag-Leffler Function.