Strong Converse Inequality for Left Gamma Quasi-Interpolants

Abstract

The rate of convergence for the Gamma operators cannot be faster than O( 1 n ). In order to obtain much faster convergence, quasi-interpolants in the sense of Sablonnière are considered. For the first time in the theory of quasi-interpolants, the strong converse inequality is solved in sup-norm with the K-functional K α λ (f, t 2r ) (0 ≤ λ ≤ 1, 0 < α < 2r).

A characterization of weighted approximations by the Post-Widder and the Gamma operators

“…In [6] we gave a brief summary of the results related to the rate of global convergence in terms of weighted K-functionals and contained in [3,7,10,12,13]. In this paper we continue this line of investigations.…”