Aldaz-Kounchev-Render operators on simplices

Ana-Maria Acu,Stefano De Marchi,Ioan Rasa

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS（2024）

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摘要

We introduce the Aldaz-Kounchev-Render operators on a multidimensional simplex. In the case of the unit simplex of Rm these operators preserve the functions 1, xj1, ... , xjm, j a positive integer. The Voronovskaja formula, the behaviour with respect to the convex function, and the limit of iterates of the operators are investigated. (c) 2024 Elsevier Inc. All rights reserved.

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关键词

Aldaz-Kounchev-Render operators,Bernstein operator,Iterates of Markov operators,Convex functions

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