Approximation Results for a General Class of Kantorovich Type Operators

By Gianluca Vinti, Luca Zampogni. 2014

52 citations recorded by the source corpus.

Abstract We introduce and study a family of integral operators in the Kantorovich sense acting on functions defined on locally compact topological groups. We obtain convergence results for the above operators with respect to the pointwise and uniform convergence and in the setting of Orlicz spaces with respect to the modular convergence. Moreover, we show how our theory applies to several classes of integral and discrete operators, as sampling, convolution and Mellin type operators in the Kantorovich sense, thus obtaining a simultaneous approach for discrete and integral operators. Further, we obtain general convergence results in particular cases of Orlicz spaces, as Lp−spaces, interpolation spaces and exponential spaces. Finally we construct some concrete examples of our operators and we show some graphical representations.

Subfields: Applied Mathematics, Computational Mechanics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/0d706f8d707cfcbc643e6afd88454fbdb6525612

How researchers see this paper

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In Applied Mathematics

1. Anna Maria Minotti
2. Danilo Costarelli
3. Gianluca Vinti

In Statistics and Probability

1. Danilo Costarelli
2. Anna Maria Minotti
3. Gianluca Vinti

Citations in the corpus

• Approximation of discontinuous signals by sampling Kantorovich series (2015, background): “For instance, a nonlinear version of Swf has been studied in [40, 26, 39] both in continuous and Orlicz functions spaces, while a more general version of these operators have been considered in [41, 42].”