## Real Analysis Exchange

### 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.

#### Article information

Source
Real Anal. Exchange, Volume 21, Number 2 (1995), 725-731.

Dates
First available in Project Euclid: 14 June 2012

https://projecteuclid.org/euclid.rae/1339694101

Mathematical Reviews number (MathSciNet)
MR1407285

Zentralblatt MATH identifier
0879.26040

Subjects
Primary: 26A99: None of the above, but in this section

#### Citation

Borsík, Ján; Červeňanský, Jaroslav; Šalát, Tibor. Remarks on functions preserving convergence of infinite series. Real Anal. Exchange 21 (1995), no. 2, 725--731. https://projecteuclid.org/euclid.rae/1339694101