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ON A NEW CLASS OF FUNCTIONS RELATED WITH MITTAG-LEFFLER AND WRIGHT FUNCTIONS AND THEIR PROPERTIES

ON A NEW CLASS OF FUNCTIONS RELATED WITH MITTAG-LEFFLER AND WRIGHT FUNCTIONS AND THEIR PROPERTIES

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In the present paper, we define new class of functions T<sub>&#x03B1;,&#x03B2;</sub>(&#x03BB;; 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&#xE1;n-type inequalities, Lazarevi&#x107;-type inequalities and Wilker-type inequalities. Moreover, integrals formula and integral inequality for the function T<sub>&#x03B1;,&#x03B2;</sub>(&#x03BB;; z) are presented.

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