Geometric properties of a certain class of Mittag–Leffler-type functions

Date

2022

Authors

Srivastava, H.M.
Kumar, Anish
Das, Sourav
Mehrez, Khaled

Journal Title

Journal ISSN

Volume Title

Publisher

Fractal and Fractional

Abstract

The main objective of this paper is to establish some sufficient conditions so that a class of normalized Mittag–Leffler-type functions satisfies several geometric properties such as starlikeness, convexity, close-to-convexity, and uniform convexity inside the unit disk. Moreover, pre-starlikeness and k-uniform convexity are discussed for these functions. Some sufficient conditions are also derived so that these functions belong to the Hardy spaces Hp and H∞. Furthermore, the inclusion properties of some modified Mittag–Leffler-type functions are discussed. The various results, which are established in this paper, are presumably new, and their importance is illustrated by several interesting consequences and examples. Some potential directions for analogous further research on the subject of the present investigation are indicated in the concluding section.

Description

Keywords

Mittag-Leffler-type functions, univalent functions, analytic functions, starlike functions, convex functions, close-to-convex functions, Fox-Wright function, Bessel-Wright function, general Wright function, Srivastava Mittag-Leffler-type functions

Citation

Srivastava, H., Kumar, A., Das, S., & Mehrez, K. (2022). “Geometric properties of a certain class of Mittag–Leffler-type functions.” Fractal and Fractional, 6(2), 54. https://doi.org/10.3390/fractalfract6020054