Approximation in the weighted generalized lipschitz class by deferred cesÁro-matrix product submethods

Abstract

In this study we obtain the error estimates of approximation to conjugate of a function f (2?-periodic) in the weighted generalized Lipschitz class W (Lp, ?(t)), p ? 1, by using a new product mean of its conjugate Fourier series. We write f ? W (Lp, ?(t)) if the condition (Formula Presented) holds, where ?(t) is a positive increasing function and p ? 1, ? ? 0. Here we introduce a new product mean called deferred Cesáro-Matrix (DCM) mean. Let T = (uj,k) be an infinite triangular matrix satisfying the Silverman-Toeplitz conditions. Then the deferred Cesáro-Matrix mean is defined by (Formula Presented) where a = (an) and b = (bn) are sequences of nonnegative integers with conditions an < bn, n = 1, 2, 3, … and lim n??bn = +?, and sk (f; x) denotes kth partial sum of Fourier series of f. © Palestine Polytechnic University-PPU 2021.