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Korovkin-type Theorems and Approximation by Positive Linear Operators

Keywords: Korovkin-type theorem , positive operator , approximation by positive operators , Stone-Weierstrass theorem , (weighted) continuous function space , Lp-space.

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Abstract:

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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