Linear methods for summing fourier series and approximation in weighted lebesgue spaces with variable exponents

In the present work, we study the estimates for the periodic functions of linear operators constructed on the basis of their Fourier series in weighted Lebesgue spaces with variable exponent and Muckenhoupt weights. In this case, the obtained estimates depend on the sequence of the best approximation in weighted Lebesgue spaces with variable exponent. Ó 2015 Springer Science+Business Media New York