On approximation properties of a family of linear operators at critical value of parameter

WOS: 000235744200008We introduce the family of linear operators [GRAPHICS] associated to a certain "admissible bunch" of operators S-t, t > 0, acting on L-p (R-n, dm, and investigate the approximation properties of this family as alpha -> 0(+). We give some applications to the Riesz and the Bessel potentials generated by the ordinary (Euclidean) and generalized translations. (C) 2005 Elsevier Inc. All rights reserved

Approximation properties of Szasz-Mirakyan-Kantorovich type operators

ARAL, Ali/0000-0002-2024-8607WOS: 000503431300011In this paper, we introduce and study new type Szasz-Mirakyan-Kantorovich operators using a technique different from classical one. This allow to analyze the mentioned operators in terms of exponential test functions instead of the usual polynomial type functions. As a first result, we prove Korovkin type approximation theorems through exponential weighted convergence. The rate of convergence of the operators is obtained for exponential weights