On a certain class of approximation operators


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.


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


approximation process; Kantorovich operator; Bernstein-Sheffer operator; r-th modulus of smoothness in Lp space

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


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