International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 21, Pages 3521-3526
doi:10.1155/IJMMS.2005.3521

A note on self-extremal sets in Lp(Ω) spaces

Viet Nguyen-Khac1 and Khiem Nguyen-Van2

1Institute of Mathematics, Vietnamese Academy of Science and Technology, 18 Hoang Quoc Viet Road, Hanoi 10307, Vietnam
2Department of Mathematics & Informatics, Hanoi University of Education, Cau Giay District, Hanoi, Vietnam

Received 24 November 2004; Revised 25 August 2005

Copyright © 2005 Viet Nguyen-Khac and Khiem Nguyen-Van. 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 give a necessary condition for a set in Lp(Ω) spaces (1<p<∞) to be self-extremal that partially extends our previous results to the case of Lp spaces. Examples of self-extremal sets in Lp(Ω)(1<p<∞) are also given.