Abstract Korovkin-type theorems in modular spaces and applications

Carlo Bardaro ; Antonio Boccuto ; Xenofon Dimitriou ; Ilaria Mantellini

Open Mathematics, Tome 11 (2013), p. 1774-1784 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Détail

Publié le : 2013-01-01

Zbl 1283.41018

EUDML-ID : urn:eudml:doc:268937

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