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 On a new class of functions related with Mittag-Leffler and Wright functions and their properties Commun. Korean Math. Soc.Published online August 28, 2020 Deepak Bansal and khaled Mehrez University College of Engineering and Technology, Bikaner, Universit\'e Tunis El Manar Abstract : In the present paper, we define new class of functions $T_{\alpha, \beta}(\lambda;z)$ 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 inequlaities. MSC numbers : 33E12, 26D07 Full-Text :