Certain geometric properties of Mittag-Leffler functions

Abstract

Abstract In this paper, some geometric properties of normalized Mittag-Leffler functions are investigated. We focus on starlikeness of order 2μ+η−1 $2\mu +\eta -1$ and convexity in the direction of imaginary axis. In addition, we study pre-starlikeness of Mittag-Leffler functions. The results are obtained by using the positivity technique.

Keywords

• Mittag-Leffler functions
• Starlike functions
• Close-to-convex functions
• Typically real function
• Convex functions in the direction of imaginary axis
• Pre-starlike functions