On The Degree of Approximation of Continous Functions

Abstract

In this paper the author has obtained the degree of approximation of a 2Tc-periodic function f of the class lâp 0 0) if f (x-|-h) - f (x) = O ( I h Let {s„} be a sequence of partial sums of the given series co s n=o c,n’ where s„= c. ... + c„. Then (E, q) (q > 0) -means of {«n} are defined by ( [4], p. 180) a-3) (i+q) -n n s k=o (^) q” The (E, q) means for q> O are regular ( [4], p. 179). Throughout this paper K’s vdll denote pofitive constants. 2. INTRODUCTION. The folJowİDg theorem on. the degree of approximation of a function f, beîongingto the class Lip a. by the (C, S) - means of its Fourifr series is proved by Alexits ([l],p.301):