Simultaneous approximation in lebesgue space with variable exponent

Abstract

In this paper we deal with the simultaneous approximations by trigonometric polynomials of 27 periodic functions in the variable exponent Lebesgue spaces. In terms of the higher moduli of smoothness the direct and inverse theorems of simultaneous approximation are proved. Moreover, the generalized variable exponent Lipschitz classes are defined and the constructive characterizations of these classes are obtained.