Abstract
In this paper we investigate some properties of approximation polynomials in particular de la Vallee-Poussin means, Fejer means and partial sums of Fourier series in weighted Lebesgue spaces with variable exponent. In addition to these we prove a simultaneous type theorem and some theorems on the equivalence of modulus of smoothness and the K-functional in weighted Lebesgue space with variable exponent.
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