DEGREE OF APPROXIMATION OF A FUNCTION ASSOCIATED WITH HARDY-LITTLEWOOD SERIES IN WEIGHTED ZYGMUND W(Z_{r}^{ω})-CLASS USING EULER-HAUSDORFF SUMMABILITY MEANS

Abstract

Approximation of functions of Lipschitz and Zygmund classes have been considered by various researchers under different summability means. In the proposed study, we investigated an estimation of the order of convergence of a function associated with Hardy-Littlewood series in the weighted Zygmund class W(Z_{r}^{ω})-class by applying Euler-Hausdorff summability means and subsequently established some (presumably new) results. Moreover, the results obtained here represent the generalization of several known results.