An Ikehara-type theorem for functions convergent to zero

TL;DR

This paper extends the Ikehara theorem to positive non-increasing functions that tend to zero, broadening the scope of asymptotic analysis in mathematical functions.

Contribution

It provides a new Ikehara-type theorem applicable to functions converging to zero, generalizing previous results by Diekmann, Kaper, Carr, and Chmaj.

Findings

Established an Ikehara-type theorem for functions converging to zero

Generalized previous asymptotic results in nonlinear analysis

Applicable to a broader class of functions in mathematical analysis

Abstract

We prove an analogue of the Ikehara theorem for positive non-increasing functions convergent to zero, generalising the results postulated in Diekmann, Kaper (1978, Nonlinear Anal. 2(6), 721--737) and Carr, Chmaj (2004, Proc. AMS 132(8), 2433--2439).