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Korovkin-type Theorems and Approximation by Positive Linear Operators

Author(s): Francesco Altomare

Journal: Surveys in Approximation Theory
ISSN 1555-578X

Volume: 5;
Start page: 92;
Date: 2010;
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Keywords: Korovkin-type theorem | positive operator | approximation by positive operators | Stone-Weierstrass theorem | (weighted) continuous function space | Lp-space.

This survey paper contains a detailed self-contained introduction to Korovkin-type theorems and to some of their applications concerning the approximation of continuous functions as well as of L_p-functions, by means of positive linear operators. The paper also contains several new results and applications. Moreover, the organization of the subject follows a simple and direct approach which quickly leads both to the main results of the theory and to some new ones.
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