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Quantitative approximation by Stancu-Durrmeyer-Choquet-Šipoš operators

  • Sorin G. Gal EMAIL logo
Published/Copyright: May 21, 2019
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Abstract

In this paper we present general quantitative estimates in terms of the modulus of continuity and of a K-functional, in approximation by the generalized multivariate Stancu-Durrmeyer-Choquet-Šipoš operators Mn,Γn,x(β,γ), with 0 ≤ βγ, written in terms of Choquet and Šipoš integrals with respect to a family of monotone and submodular set functions, Γn, x, on the standard d-dimensional simplex. If d = 1 and the Choquet integrals are taken with respect to some concrete possibility measures, the estimate in terms of the modulus of continuity is detailed. Examples improving the estimates given by the classical operators also are presented.

  1. (Communicated by Anatolij Dvurečenskij)

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Received: 2018-02-27
Accepted: 2018-08-03
Published Online: 2019-05-21
Published in Print: 2019-06-26

© 2019 Mathematical Institute Slovak Academy of Sciences

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