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