Rates of approximation for general sampling-type operators in the setting of filter convergence

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Rates of approximation for general sampling-type operators in the setting of filter convergence

We investigate the order of approximation of a real-valued function f by means of suitable families of sampling type operators, which include both discrete and integral ones. 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 deal with filter convergence, obtaining proper extensions of classical results

Rates of approximation for general sampling-type operators in the setting of filter convergence

We investigate the order of approximation of a real-valued function f by means of suitable families of sampling type operators, which include both discrete and integral ones. 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 deal with filter convergence, obtaining proper extensions of classical results.©2013 The Authors. Published by Elsevier Inc. All rights reserved