Approximation theorems in weighted Lebesgue spaces with variable exponent

Abstract

In this work, approximation properties of de la Vall?e-Poussin means are investigated in weighted Lebesgue spaces with variable exponent where weight function belongs to Muckenhoupt class. For this purpose direct, inverse and simultaneous theorems of approximation theory are proved and constructive characterizations of functions are obtained in weighted Lebesgue spaces with variable exponent.

Near best approximation property of interpolation and Poisson polynomials in weighted variable exponent Smirnov classes

“…The following theorem in the case of r = 1 was proved in [33]. For r > 1 it can be proved using [34] by similar way.…”