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Some versions of limit and Dieudonné-type theorems with respect to filter convergence for (ℓ)-group-valued measures

100%

Boccuto A. , Dimitriou X. , Papanastassiou N.

Open Mathematics

2011

tom 9

nr 6

1298-1311

Some limit and Dieudonné-type theorems in the setting of (ℓ)-groups with respect to filter convergence are proved, extending earlier results.

Abstract Korovkin-type theorems in modular spaces and applications

100%

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.