Functions and Analysis

    

Recent Results on Modular Convergence Theorems, Rates of Approximation and Korovkin Theorems for Filter Convergence

Authors: Antonio Boccuto, Xenofon Dimitriou

We give a survey on recent results about the problem of approximating a real-valued function by means of suitable families of sampling type operators, which include both discrete and integral ones, and about the order of approximation, and abstract Korovkin-type theorems with respect to different types of test functions, in the context of filter convergence. We give a unified approach, by means of which it is possible to consider several kinds of classical operators, for instance Urysohn integral operators, in particular Mellin-type convolution integrals, and generalized sampling series. We obtain proper extensions of classical results.

Comments: 9 Pages.

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Submission history

[v1] 2014-03-27 10:50:26

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