Banach Journal of Mathematical Analysis

A generalization of Kantorovich operators for convex compact subsets

Francesco Altomare, Mirella Cappelletti Montano, Vita Leonessa, and Ioan Raşa

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Abstract

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.

Article information

Source
Banach J. Math. Anal., Volume 11, Number 3 (2017), 591-614.

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

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1494036023

Digital Object Identifier
doi:10.1215/17358787-2017-0008

Mathematical Reviews number (MathSciNet)
MR3679897

Zentralblatt MATH identifier
1383.41003

Subjects
Primary: 47B65: Positive operators and order-bounded operators
Secondary: 41A36: Approximation by positive operators

Keywords
Markov operator positive approximation process Kantorovich operator preservation property

Citation

Altomare, Francesco; Cappelletti Montano, Mirella; Leonessa, Vita; Raşa, Ioan. A generalization of Kantorovich operators for convex compact subsets. Banach J. Math. Anal. 11 (2017), no. 3, 591--614. doi:10.1215/17358787-2017-0008. https://projecteuclid.org/euclid.bjma/1494036023


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