Monotonicity Properties and functional inequalities for the Volterra and 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 Turán type inequalities) as well as we determined sharp upper and lower bounds for the normalized incomplete Volterra functions in terms of weighted power means.

Submitted to Integral Transforms and Special Functions. In this version acknowledgement is added and some references are corrected