A survey on recent results in Korovkin’s approximation theory in modular spaces

Ilaria Mantellını; Antonio Boccuto; Carlo Bardaro

doi:10.33205/cma.804697

Research Article

A survey on recent results in Korovkin’s approximation theory in modular spaces

Year 2021, Volume: 4 Issue: 1, 48 - 60, 01.03.2021

Ilaria Mantellını Antonio Boccuto Carlo Bardaro

https://doi.org/10.33205/cma.804697

Cited By: 2

Abstract

In this paper we give a survey about recent versions of Korovkin-type theorems for modular function spaces, a class which includes $L^p$, Orlicz, Musielak-Orlicz spaces and many others. We consider various kinds of modular convergence, using certain summability processes, like triangular matrix statistical convergence, and filter convergence (which are generalizations of the statistical convergence). Finally, wwe consider an abstract axiomatic convergence which includes the previous ones and even almost convergence, which is not generated by any filter, as we show by an example.

Keywords

Korovkin's theorem, modular space, filter convergence, abstract convergence

Supporting Institution

Gruppo Nazionale per l'Analisi Matematica e Applicazioni (GNAMPA)'' of the ``Instituto nazionale di alta matematica (INDAM)'' `

Project Number

not applicable

Thanks

Dedicated to Professor Francesco Altomare on occasion of his 70th Birthday

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