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- Title
Quantitative approximation by Stancu-Durrmeyer-Choquet-Šipoš operators.
- Authors
Gal, Sorin G.
- 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 M n , Γ n , x (β , γ) $\begin{array}{} M_{n, \Gamma_{n, x}}^{(\beta, \gamma)} \end{array} $ , with 0 ≤ β ≤ γ, 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.
- Subjects
APPROXIMATION theory; CHOQUET theory; MONOTONE operators; SUBMODULAR functions; BOREL subsets
- Publication
Mathematica Slovaca, 2019, Vol 69, Issue 3, p625
- ISSN
0139-9918
- Publication type
Article
- DOI
10.1515/ms-2017-0252