Abstract Korovkin-type theorems in modular spaces and applications

By Carlo Bardaro, Antonio Boccuto, Xenofon Dimitriou, Ilaria Mantellini. 2013

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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.

Subfields: Applied Mathematics, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/77b402edb25ea563ec66adbc1d3591c94299c7a4