Abstract Korovkin-type theorems in modular spaces and applications

• Autorzy: Carlo Bardaro , Antonio Boccuto , Xenofon Dimitriou , Ilaria Mantellini
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 40A35: Ideal and statistical convergence
• 41A35: Approximation by operators (in particular, by integral operators)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 10
• Strony: 1774-1784

Daty

wydano

2013-10-01

online

2013-07-20

Twórcy

autor

Carlo Bardaro

• Department of Mathematics and Computer Sciences, University of Perugia, via Vanvitelli 1, 06123, Perugia, Italy

autor

Antonio Boccuto

• Department of Mathematics and Computer Sciences, University of Perugia, via Vanvitelli 1, 06123, Perugia, Italy

autor

Xenofon Dimitriou

• Department of Mathematics, University of Athens, Panepistimiopolis, Athens, 15784, Greece

autor

Ilaria Mantellini

• Department of Mathematics and Computer Sciences, University of Perugia, via Vanvitelli 1, 06123, Perugia, Italy

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-013-0288-7