A generalization of Kantorovich operators for convex compact subsets
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
Cite
@article{arxiv.1605.06768,
title = {A generalization of Kantorovich operators for convex compact subsets},
author = {Francesco Altomare and Mirella Cappelletti Montano and Vita Leonessa and Ioan Rasa},
journal= {arXiv preprint arXiv:1605.06768},
year = {2017}
}
Comments
Research article