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
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 H. Vaezi and S. F. Rzaev. 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(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.