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Commun. Korean Math. Soc. 2020; 35(4): 1123-1132
Online first article August 28, 2020 Printed October 31, 2020
https://doi.org/10.4134/CKMS.c200022
Copyright © The Korean Mathematical Society.
On a new class of functions related with Mittag-Leffler and Wright functions and their properties
Deepak Bansal, Khaled Mehrez
College of Engg. and Technology; Facult\'e des sciences de Tunis
In the present paper, we define new class of functions \linebreak $T_{\alpha, \beta}(\lambda;z)$ which is an extension of the classical Wright function and the Mittag-Leffler function. We show some mean value inequalities for the this function, such as Tur\'{a}n-type inequalities, Lazarevi\'{c}-type inequalities and Wilker-type inequalities. Moreover, integrals formula and integral inequality for the function $T_{\alpha, \beta}(\lambda;z)$ are presented.
Keywords: Wright function, Mittag-Leffler function, Tur\'{a}n type inequalities, Lazarevi\'{c}-type inequalities, Wilker-type inequalities
MSC numbers: 33E12, 26D07
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