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Open Mathematics

formerly Central European Journal of Mathematics

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

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Abstract Korovkin-type theorems in modular spaces and applications

Carlo Bardaro
  • Department of Mathematics and Computer Sciences, University of Perugia, via Vanvitelli 1, 06123, Perugia, Italy
  • :
/ Antonio Boccuto
  • Department of Mathematics and Computer Sciences, University of Perugia, via Vanvitelli 1, 06123, Perugia, Italy
  • :
/ Xenofon Dimitriou
  • Department of Mathematics, University of Athens, Panepistimiopolis, Athens, 15784, Greece
  • :
/ Ilaria Mantellini
  • Department of Mathematics and Computer Sciences, University of Perugia, via Vanvitelli 1, 06123, Perugia, Italy
  • :
Published Online: 2013-07-20 | DOI: https://doi.org/10.2478/s11533-013-0288-7

Abstract

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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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, July 2013

© 2013 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

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