Tur\'an type inequalities for classical and generalized Mittag-Leffler functions

TL;DR

This paper establishes Turán type inequalities for classical and generalized Mittag-Leffler functions using monotonicity methods, with applications to related inequalities and open problems in the field.

Contribution

It introduces new Turán type inequalities for Mittag-Leffler functions and applies them to Lazarević and Wilker-type inequalities, expanding the theoretical understanding of these functions.

Findings

Derived new Turán inequalities for Mittag-Leffler functions

Applied inequalities to Lazarević and Wilker-type bounds

Proposed open problems for future research

Abstract

In this paper some Tur\'an type inequalities for classical and generalized Mittag-Leffler functions are considered. The method is based on proving monotonicity for special ratio of sections for series of Mittag-Leffler functions. Some applications are considered to Lazarevi\'c and Wilker-type inequalities for classical and generalized Mittag-Leffler functions. At the end some open problems are formulated.