Monotonicity Properties and functional inequalities for the Volterra and incomplete Volterra functions

TL;DR

This paper investigates the monotonicity, convexity, and concavity properties of Volterra functions, deriving functional inequalities and bounds that enhance understanding of their mathematical behavior.

Contribution

It introduces new monotonicity and convexity properties for Volterra functions and establishes sharp bounds and inequalities, advancing theoretical knowledge in this area.

Findings

Proved monotonicity, log-convexity, and log-concavity of Volterra functions

Derived functional inequalities including Turán type inequalities

Established sharp bounds for normalized incomplete Volterra functions

Abstract

In this paper we prove some monotonicity, log--convexity and log--concavity properties for the Volterra and incomplete Volterra functions. Moreover, as consequences of these results, we present some functional inequalities (like Tur\'an type inequalities) as well as we determined sharp upper and lower bounds for the normalized incomplete Volterra functions in terms of weighted power means.