Abstract
In this paper our aim is to present the completely monotonicity and convexity properties for the Wright function. As consequences of these results, we present some functional inequalities. Moreover, we derive the monotonicity and log-convexity results for the generalized Wright functions. As applications, we present several new inequalities (like Turan type inequalities) and we prove some geometric properties for four--parametric Mittag--Leffler functions.
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