## 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

### Keywords:

convergence-preserving functions
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