Functional inequalities for Fox-Wright functions

TL;DR

This paper establishes various mean value inequalities, including Turán-type and Wilker-type inequalities, for Fox-Wright functions and related special functions, with applications to hypergeometric and Mittag-Leffler functions.

Contribution

It introduces new inequalities and monotonicity results for Fox-Wright functions, extending classical inequalities to a broader class of special functions.

Findings

Derived Turán-type inequalities for Fox-Wright functions

Proved monotonicity of ratios for series sections of Fox-Wright functions

Established new inequalities for hypergeometric and Mittag-Leffler functions

Abstract

In this paper, our aim is to show some mean value inequalities for the Fox-Wright functions, such as Tur\'an--type inequalities, Lazarevi\'c and Wilker--type inequalities. As applications we derive some new type inequalities for hypergeometric functions and the four--parametric Mittag--Leffler functions. Furthermore, we prove monotonicity of ratios for sections of series of Fox-Wright functions, the results is also closely connected with Tur\'an--type inequalities. Moreover, some other type inequalities are also presented. At the end of the paper, some problems stated, which may be of interest for further research.