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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

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Volume 11, Issue 10


Volume 13 (2015)

Abstract Korovkin-type theorems in modular spaces and applications

Carlo Bardaro / Antonio Boccuto / Xenofon Dimitriou / Ilaria Mantellini
Published Online: 2013-07-20 | DOI: https://doi.org/10.2478/s11533-013-0288-7


We prove some versions of abstract Korovkin-type theorems in modular function spaces, with respect to filter convergence for linear positive operators, by considering several kinds of test functions. We give some results with respect to an axiomatic convergence, including almost convergence. An extension to non positive operators is also studied. Finally, we give some examples and applications to moment and bivariate Kantorovich-type operators, showing that our results are proper extensions of the corresponding classical ones.

MSC: 40A35; 41A35; 46E30

Keywords: Modular space; Linear operator; Korovkin theorem; Filter convergence; Almost convergence

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About the article

Published Online: 2013-07-20

Published in Print: 2013-10-01

Citation Information: Open Mathematics, Volume 11, Issue 10, Pages 1774–1784, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/s11533-013-0288-7.

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