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International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 20, Pages 1251-1260
http://dx.doi.org/10.1155/S0161171203204269

Modulus of smoothness and theorems concerning approximation on compact groups

1Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
2Institute of Mathematics and Mechanics, Azerbaijan Academy of Sciences, Baku, Azerbaijan

Received 3 April 2002

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the generalized shift operator defined by (Shuf)(g)=Gf(tut1g)dt on a compact group G, and by using this operator, we define “spherical” modulus of smoothness. So, we prove Stechkin and Jackson-type theorems.