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Korovkin theorem in modular spaces

100%

Bardaro C. , Mantellini I.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2007

tom Vol. 47, [Z] 2

239-253

In this paper we obtain an extension of the classical Korovkin theorem in abstract modular spaces. Applications to some discrete and integral operators are discussed.

Statistical approximation in multivariate modular function spaces

100%

Belen C. , Yildirim M.

Commentationes Mathematicae

2011

tom Vol. 51, [Z] 1

39-53

In this paper, using the concept of A-statistical convergence we prove a Korovkin type approximation theorem in multivariate modular function spaces. Furthermore, giving an example via bivariate operators of Kantorovich type, it is shown that our theorem is stronger than its classical case.

Korovkin theorem in modular spaces

100%

Bardaro C. , Mantellini I.

Commentationes Mathematicae

2007

tom 47

nr 2

In this paper we obtain an extension of the classical Korovkin theorem in abstract modular spaces. Applications to some discrete and integral operators are discussed.

Abstract Korovkin-type theorems in modular spaces and applications

88%

Bardaro C. , Boccuto A. , Dimitriou X. , Mantellini I.

Open Mathematics

2013

tom 11

nr 10

1774-1784

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.