Abstract Korovkin-type theorems in modular spaces and applications

Abstract Korovkin-type theorems in modular spaces and applications Abstract 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Open Mathematics de Gruyter

Abstract Korovkin-type theorems in modular spaces and applications

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Publisher
de Gruyter
Copyright
Copyright © 2013 by the
eISSN
2391-5455
D.O.I.
10.2478/s11533-013-0288-7
Publisher site
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Abstract

Abstract 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.

Journal

Open Mathematicsde Gruyter

Published: Oct 1, 2013

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