Abstract Korovkin-type theorems in modular spaces and applications

Carlo Bardaro; Antonio Boccuto; Xenofon Dimitriou; Ilaria Mantellini

Open Mathematics (2013)

  • Volume: 11, Issue: 10, page 1774-1784
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Carlo Bardaro, et al. "Abstract Korovkin-type theorems in modular spaces and applications." Open Mathematics 11.10 (2013): 1774-1784. <http://eudml.org/doc/268937>.

@article{CarloBardaro2013,
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.},
author = {Carlo Bardaro, Antonio Boccuto, Xenofon Dimitriou, Ilaria Mantellini},
journal = {Open Mathematics},
keywords = {Modular space; Linear operator; Korovkin theorem; Filter convergence; Almost convergence; modular space; linear operator; filter convergence; almost convergence},
language = {eng},
number = {10},
pages = {1774-1784},
title = {Abstract Korovkin-type theorems in modular spaces and applications},
url = {http://eudml.org/doc/268937},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Carlo Bardaro
AU - Antonio Boccuto
AU - Xenofon Dimitriou
AU - Ilaria Mantellini
TI - Abstract Korovkin-type theorems in modular spaces and applications
JO - Open Mathematics
PY - 2013
VL - 11
IS - 10
SP - 1774
EP - 1784
AB - 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.
LA - eng
KW - Modular space; Linear operator; Korovkin theorem; Filter convergence; Almost convergence; modular space; linear operator; filter convergence; almost convergence
UR - http://eudml.org/doc/268937
ER -

References

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