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Korovkin-type Theorems for Abstract Modular Convergence

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Abstract

We give some Korovkin-type theorems on convergence and estimates of rates of approximations of nets of functions, satisfying suitable axioms, whose particular cases are filter/ideal convergence, almost convergence and triangular A-statistical convergence, where A is a non-negative summability method. Furthermore, we give some applications to Mellin-type convolution and bivariate Kantorovich-type discrete operators.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, University of Perugia, via Vanvitelli, 1, 06123, Perugia, Italy

    Antonio Boccuto

  2. Department of Mathematics, University of Athens, Panepistimiopolis, 15784, Athens, Greece

    Xenofon Dimitriou

Authors
  1. Antonio Boccuto
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  2. Xenofon Dimitriou
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Correspondence to Antonio Boccuto.

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Boccuto, A., Dimitriou, X. Korovkin-type Theorems for Abstract Modular Convergence. Results. Math. 69, 477–495 (2016). https://doi.org/10.1007/s00025-016-0536-9

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  • DOI: https://doi.org/10.1007/s00025-016-0536-9

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