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