Real Analysis Exchange

Remarks on functions preserving convergence of infinite series

Ján Borsík, Jaroslav Červeňanský, and Tibor Šalát

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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

Permanent link to this document
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

Keywords
preserving convergence of infinite series Baire category

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


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