Monotonicity patterns and functional inequalities for classical and generalized Wright functions

TL;DR

This paper investigates the monotonicity and convexity properties of Wright and generalized Wright functions, deriving new inequalities and geometric properties for related special functions.

Contribution

It introduces new monotonicity, convexity, and inequality results for Wright and generalized Wright functions, including applications to Mittag-Leffler functions.

Findings

Established complete monotonicity and convexity properties.

Derived new functional inequalities, including Turán-type inequalities.

Proved geometric properties for four-parametric Mittag-Leffler functions.

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 Tur\'an type inequalities) and we prove some geometric properties for four--parametric Mittag--Leffler functions.