Open Access
July 2017 A generalization of Kantorovich operators for convex compact subsets
Francesco Altomare, Mirella Cappelletti Montano, Vita Leonessa, Ioan Raşa
Banach J. Math. Anal. 11(3): 591-614 (July 2017). DOI: 10.1215/17358787-2017-0008


In this article, 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 Borel probability measures. By considering special cases of these parameters for particular convex compact subsets, we obtain the classical Kantorovich operators defined in the 1-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, we discuss the preservation of Lipschitz-continuity and of convexity.


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Francesco Altomare. Mirella Cappelletti Montano. Vita Leonessa. Ioan Raşa. "A generalization of Kantorovich operators for convex compact subsets." Banach J. Math. Anal. 11 (3) 591 - 614, July 2017.


Received: 16 July 2016; Accepted: 19 September 2016; Published: July 2017
First available in Project Euclid: 6 May 2017

zbMATH: 1383.41003
MathSciNet: MR3679897
Digital Object Identifier: 10.1215/17358787-2017-0008

Primary: 47B65
Secondary: 41A36

Keywords: Kantorovich operator , Markov operator , positive approximation process , preservation property

Rights: Copyright © 2017 Tusi Mathematical Research Group

Vol.11 • No. 3 • July 2017
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