Remarks on functions preserving convergence of infinite series

Abstract

A function \(f:\: \mathbb{R}\to\mathbb{R}\) preserves absolute convergence of series if for each absolutely convergent series \(\sum_{n=1}^{\infty} a_n\) its \(f\)-transform \(\sum_{n=1}^{\infty} f(a_n)\) is absolutely convergent. In this note, we shall study functions that preserve absolute convergence of series.