Banach Journal of Mathematical Analysis

Two Korovkin-type theorems in multivariate approximation

Allal Guessab and Gerhard Schmeisser

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Abstract

Let $\Omega$ be a compact convex subset of $\R^d$ and let $(L_n)_{n\in\N}$ be a sequence of positive linear operators that map $C(\Omega)$ into itself. We establish two Korovkin-type theorems in which the limit of the sequence of operators is not necessarily the identity.

Article information

Source
Banach J. Math. Anal., Volume 2, Number 2 (2008), 121-128.

Dates
First available in Project Euclid: 21 April 2009

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1240336298

Digital Object Identifier
doi:10.15352/bjma/1240336298

Mathematical Reviews number (MathSciNet)
MR2436872

Zentralblatt MATH identifier
1155.41008

Subjects
Primary: 41A36: Approximation by positive operators
Secondary: 41A63: Multidimensional problems (should also be assigned at least one other classification number in this section) 26B25: Convexity, generalizations

Keywords
Korovkin-type theorems positive linear operator convexity

Citation

Guessab, Allal; Schmeisser, Gerhard. Two Korovkin-type theorems in multivariate approximation. Banach J. Math. Anal. 2 (2008), no. 2, 121--128. doi:10.15352/bjma/1240336298. https://projecteuclid.org/euclid.bjma/1240336298


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