On The Degree of Approximation of Continous Functions

Year 1981, Volume: 30 , 0 - 0, 01.01.1981

Chandra Prem

https://doi.org/10.1501/Commua1_0000000095

Abstract

In this paper the author has obtained the degree of approximation of a 2Tc-periodic function f of the class lâp 00) 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):

Keywords

Degree, Approximation, Continous Functions

References

• Ankara Üniversitesi – Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Dergisi