Properties of a new class of recursively defined Baskakov-type operators

Octavian Agratini

Address. Babes-Bolyai University, Faculty of Mathematics and Informatics, Kogalniceanu 1, RO-3400 Cluj-Napoca, ROMANIA


Abstract. By starting from a recent paper by Campiti and Metafune [7], we consider a generalization of the Baskakov operators, which is introduced by replacing the binomial coefficients with other coefficients defined recursively by means of two fixed sequences of real numbers. In this paper, we indicate some of their properties, including a decomposition into an expression which depends linearly on the fixed sequences and an estimation of the corresponding order of approximation, in terms of the modulus of continuity.

AMSclassification. 41A35, 41A25, 26D15

Keywords. Baskakov-type operators, order of approximation, modulus of continuity