A GENERALIZATION OF KANTOROVICH OPERATORS FOR CONVEX COMPACT SUBSETS

被引：26

作者：

Altomare, Francesco ^{[1
]}

Cappelletti Montano, Mirella ^{[1
]}

Leonessa, Vita ^{[2
]}

Rasa, Ioan ^{[3
]}

机构：

[1] Univ Bari Aldo Moro, Dipartimento Matemat, Campus Univ,Via E Orabona 4, I-70125 Bari, Italy

[2] Univ Basilicata, Dipartimento Matemat Informat & Econ, Viale Ateneo Lucano 10,Campus Macchia Romana, I-85100 Potenza, Italy

[3] Tech Univ Cluj Napoca, Dept Math, Str Memrandumului 28, RO-400114 Cluj Napoca, Romania

来源：

BANACH JOURNAL OF MATHEMATICAL ANALYSIS | 2017年 / 11卷 / 03期

关键词：

Markov operator; positive approximation process; Kantorovich operator; preservation property; POSITIVE LINEAR-OPERATORS;

D O I：

10.1215/17358787-2017-0008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we introduce and study a new sequence of positive linear operators acting on function spaces de fined 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 de fined 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.

引用

页码：591 / 614

页数：24

共 18 条

[1]

Adams R. A., 1975, PURE APPL MATH, V65

[2]

Altomare F, 2014, DEGRUYTER STUD MATH, V61, P1

[3]

Altomare F., 1994, KOROVKIN TYPE APPROX, V17

[4] On differential operators associated with Markov operators [J].