On a certain class of approximation operators

Abstract

The paper is devoted to the study of an approximation process $$K_{n}^{H}$$ representing an integral form in Kantorovich sense of Bernstein-Sheffer operators. We establish the degree of approximation both in $$C\left[ 0,1\right]$$ space in terms of the modulus of continuity and $$L_{p}\left[0,1\right] ,p\geq1$$, spaces in terms of the integral modulus of smoothness. Consequently, it results that the sequence $$\left( K_{n}^{H}\right)_{n\geq1}$$ converges to the indentity operator in the mentioned spaces. Also we point out a connection between the smoothness of local Lipschitz $$-\alpha\left( 0<\alpha\leq1\right)$$ functions and the local approximating property.

Authors

Octavian Agratini
Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania

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Paper coordinates

O. Agratini, On a certain class of approximation operators, Pure Mathematics and Applications, 11 (2000) no. 2, pp. 119-127

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