On Approximation of Functions Belonging to Lip(α, r) Class and to Weighted W(Lr,ξ(t)) Class by Product Mean

Abstract

A good amount of work has been done on degree of approximation of functions belonging to Lip, Lip((t),r) and W() and classes using Cesro, Nrlund and generalised Nrlund single summability methods by a number of researchers ([1], [10], [8], [6], [7], [2], [3], [4], [9]). But till now, nothing seems to have been done so far to obtain the degree of approximation of functions using (N,)(C, 1) product summability method. Therefore the purpose of present paper is to establish two quite new theorems on degree of approximation of function class and class by (N, )(C, 1) product summability means of its Fourier series.