Korovkin-type Theorems and Approximation by Positive Linear Operators

By Francesco Altomare. 2010

159 citations recorded by the source corpus.

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. MSC: 41A36, 46E05, 47B65

Subfields: Applied Mathematics, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/395950a2c232680d75575821c86d954df466c192

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Citations in the corpus

Statistical Convergence with Respect to Power Series Methods and Applications to Approximation Theory (2019, background): “Recall that Korovkin type approximation theory deals with the convergence of the sequences of the positive linear operators to the identity operator [15, 16].”
A certain class of weighted statistical convergence and associated Korovkin‐type approximation theorems involving trigonometric functions (2017, methodology): “Therefore, if we use the condition (23) in Theorem 2 instead of the conditions (i) and (ii), then we obtain the rates of the deferred weighted statistical convergence of the sequence (Lm) of positive linear operators in Theorem 1.”
Abstract Korovkin-type theorems in modular spaces and applications (2013, background): “One more set of test functions in abstract contexts was suggested in [3, 4].”