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Convergence-preserving functions. (English) Zbl 0664.40001

A function f from the reals to itself is called convergence preserving (CP) if for every convergent series \(\sum a_ n\) also \(\sum f(a_ n)\) converges. The author proves that f is CP iff \(f(x)=kx\) in a neighborhood of 0.
Reviewer: J.Smital

MSC:

40A05 Convergence and divergence of series and sequences
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