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2013 | 11 | 10 | 1774-1784
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Abstract Korovkin-type theorems in modular spaces and applications

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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.
  • Department of Mathematics and Computer Sciences, University of Perugia, via Vanvitelli 1, 06123, Perugia, Italy,
  • Department of Mathematics and Computer Sciences, University of Perugia, via Vanvitelli 1, 06123, Perugia, Italy,
  • Department of Mathematics, University of Athens, Panepistimiopolis, Athens, 15784, Greece,
  • Department of Mathematics and Computer Sciences, University of Perugia, via Vanvitelli 1, 06123, Perugia, Italy,
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