In: Mathematica Slovaca, vol. 65, no. 1
Peter Eliaš
Details:
Year, pages: 2015, 63 - 78
Keywords:
series, divergence, relative convergence
About article:
We provide a characterization of two families of real functions, namely, of those functions $f$ such that the series $∑ f(xn)$ diverges whenever the series $∑ xn$ diverges, or, respectively, whenever the series $∑ xn$ non-absolutely converges. This solves two open problems of J. Borsík. We also reformulate known results on families of functions preserving or changing the type of convergence of series, and add some results about divergent series of terms converging to zero.
How to cite:
ISO 690:
Eliaš, P. 2015. On the convergence of a series mapped by a function. In Mathematica Slovaca, vol. 65, no.1, pp. 63-78. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0007
APA:
Eliaš, P. (2015). On the convergence of a series mapped by a function. Mathematica Slovaca, 65(1), 63-78. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0007
About edition:
Published: 1. 2. 2015