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

Modulus of smoothness and theorems concerning approximation on compact groups

H. Vaezi1 and S. F. Rzaev2

 1Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
2Institute of Mathematics and Mechanics, Azerbaijan Academy of Sciences, Baku, Azerbaijan
Received 3 April 2002

Abstract

We consider the generalized shift operator defined by (Shuf)(g)=∫Gf(tut−1g)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.