Korovkin-type theorems for abstract modular convergence

2021/01/13 by Antonio Boccuto, Boccuto, Antonio, Xenofon Dimitriou +1
Mathematics · #Approximation Theory and Sequence Spaces

paper · pdf · doi:10.48550/arxiv.2101.05341

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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