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arXiv · 1605.06768

A generalization of Kantorovich operators for convex compact subsets

Francesco Altomare·Mirella Cappelletti Montano·Vita Leonessa·Ioan Rasa
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Abstract

In this paper we introduce and study a new sequence of positive linear operators acting on function spaces defined on a convex compact subset. Their construction depends on a given Markov operator, a positive real number and a sequence of probability Borel measures. By considering special cases of these parameters for particular convex compact subsets we obtain the classical Kantorovich operators defined in the one-dimensional and multidimensional setting together with several of their wide-ranging generalizations scattered in the literature. We investigate the approximation properties of these operators by also providing several estimates of the rate of convergence. Finally, the preservation of Lipschitz-continuity as well as of convexity are discussed

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Francesco Altomare, Mirella Cappelletti Montano, Vita Leonessa, Ioan Rasa. 2016-05-22. A generalization of Kantorovich operators for convex compact subsets. https://doi.org/10.1215/17358787-2017-0008

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