Geometric Properties of a Certain Class of Mittag–Leffler-Type Functions

Fractal and Fractional

Hari M. Srivastava¹  Khaled Mehrez²  Sourav Das³  Anish Kumar³ 

[1] Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada;Department of Mathematics, Kairouan Preparatory Institute for Engineering Studies, University of Kairouan, Kairouan 3100, Tunisia;Department of Mathematics, National Institute of Technology Jamshedpur, Jamshedpur 831014, India;

关键词: Mittag–Leffler-type functions;    univalent functions;    analytic functions;    starlike functions;    convex functions;    close-to-convex functions;   

DOI  :  10.3390/fractalfract6020054

来源: DOAJ

【 摘 要 】

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 ${\mathcal{H}}^p$ and ${\mathcal{H}}^{\infty }$. 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.

【 授权许可】

Unknown