Monotonicity, convexity, and inequalities for functions involving gamma function

TL;DR

This paper investigates properties like monotonicity and convexity of functions combining the gamma function and power functions, generalizing existing results for various parameter values.

Contribution

It introduces new generalized results on the monotonicity and convexity of gamma-related functions, extending prior specific cases.

Findings

Established monotonicity and convexity properties for gamma-related functions.

Generalized known inequalities for broader parameter ranges.

Provided conditions under which these properties hold.

Abstract

In this paper, we study some properties such as the monotonicity, logarithmically complete monotonicity, logarithmic convexity, and geometric convexity, of the combinations of gamma function and power function. The results we obtain generalize some related known results for parameters with specific values.