Phillips-type \(q\)-Bernstein operators on triangles
type: Item
instance of: scholarly article
title: Phillips-type \(q\)-Bernstein operators on triangles
zbMATH Open document ID: 1462.41010
DOI: 10.1155/2021/6637893
author: Yanyan Li
published in: Journal of Function Spaces
publication date: 2021-05-03T00:00:00Z
review text: Summary: The purpose of the paper is to introduce a new analogue of Phillips-type Bernstein operators \((\mathcal{B}_{m,q}^u f)(u,v)\) and \((\mathcal{B}_{n,q}^v f) (u,v)\), their products \((\mathcal{P}_{mn,q}f) (u,v)\) and \((\mathcal{Q}_{nm,q}f) (u,v)\), their Boolean sums \((\mathcal{S}_{mn,q}f) (u,v)\) and \((\mathcal{T}_{nm,q}f) (u,v)\) on triangle \(\mathcal{T}_h\), which interpolate a given function on the edges, respectively, at the vertices of triangle using quantum analogue. Based on Peano's theorem and using modulus of continuity, the remainders of the approximation formula of corresponding operators are evaluated. Graphical representations are added to demonstrate consistency to theoretical findings. It has been shown that parameter \(q\) provides flexibility for approximation and reduces to its classical case for \(q=1\).
Mathematics Subject Classification ID: 41A36
zbMATH DE Number: 7341755
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/6637893
OpenAlex ID: W3132294292
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description: scientific article; zbMATH DE number 7341755