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Symmetry 2019, 11(1), 45; https://doi.org/10.3390/sym11010045

Geometric Properties of Normalized Mittag–Leffler Functions

1
Department of Mathematics, Government College University, Faisalabad 38000, Pakistan
2
Department of Mathematics, Yangzhou University, Yangzhou 225002, China
3
Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan
*
Author to whom correspondence should be addressed.
Received: 7 December 2018 / Revised: 20 December 2018 / Accepted: 24 December 2018 / Published: 3 January 2019
(This article belongs to the Special Issue Integral Transforms and Operational Calculus)
Full-Text   |   PDF [262 KB, uploaded 3 January 2019]

Abstract

The aim of this paper is to investigate certain properties such as convexity of order μ , close-to-convexity of order 1 + μ /2 and starlikeness of normalized Mittag–Leffler function. We use some inequalities to prove our results. We also discuss the close-to-convexity of Mittag–Leffler functions with respect to certain starlike functions. Furthermore, we find the conditions for the above-mentioned function to belong to the Hardy space H p . Some of our results improve the results in the literature. View Full-Text
Keywords: analytic functions; Mittag–Leffler functions; starlike functions; convex functions; Hardy space analytic functions; Mittag–Leffler functions; starlike functions; convex functions; Hardy space
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Noreen, S.; Raza, M.; Liu, J.-L.; Arif, M. Geometric Properties of Normalized Mittag–Leffler Functions. Symmetry 2019, 11, 45.

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