Quantitative approximation by Stancu-Durrmeyer-Choquet-\v{S}ipo\v{s} operators

Year, pages: 2019, 625 - 638

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-\v{S}ipo\v{s} operators $M_{n, Γn, x}^{(β, γ)}$, with $0≤ β≤ γ$, written in terms of Choquet and \v{S}ipo\v{s} integrals with respect to a family of monotone and submodular set functions, $Γ_{n, x}$, 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.

Gal, S. 2019. Quantitative approximation by Stancu-Durrmeyer-Choquet-\v{S}ipo\v{s} operators. In Mathematica Slovaca, vol. 69, no.3, pp. 625-638. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0252

Gal, S. (2019). Quantitative approximation by Stancu-Durrmeyer-Choquet-\v{S}ipo\v{s} operators. Mathematica Slovaca, 69(3), 625-638. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0252