ON A GENERALIZED CONVOLUTION APPROXIMATION PROBLEM

Sheng Baohuai (P. R. China)

Received February 6, 2009

Abstract

In the present paper, a kind of generalized convolutional approximation problem is dealt with. The Jackson inequality for such type of convolutional approximation is established for the kernels with the Jacobi polynomials being their eigenfunctions. The direct and the inverse theorems are established with a K-functional.

Keywords and phrases: learning theory, Jacobi polynomials, approximation theory, Jackson inequality, K-functional.