A STUDY ON APPROXIMATION OF A CONJUGATE FUNCTION USING CESÀRO-MATRIX PRODUCT OPERATOR

Abstract

In this paper, we establish a new theorem to study the error approximation of a function ζ̃ conjugate of a function ζ (2π-periodic) in weighted Lipschitz class W(L^p,p ≥ 1, ξ(ω)), by Cesàro-Matrix (CδT) product means of its CFS, where CFS denotes conjugate Fourier series. In fact, the results obtained in the paper provide the best approximation of the conjugate function ζ̃ in W(L^p,p ≥ 1, ξ(ω)) class by C^δT product means of its ate CFS for the cases p > 1 and p = 1. Our results generalize six previously known results. Thus, the results of [4], [11], [12], [13], [14], [15] become the particular cases of our results. Our theorems provide some important corollaries.