Journal of Inequalities and Applications
Volume 2006 (2006), Article ID 26265, 12 pages
doi:10.1155/JIA/2006/26265

The James constant of normalized norms on ℝ2

Weerayuth Nilsrakoo1,2 and Satit Saejung1

1Department of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand
2Department of Mathematics, Statistics and Computer, Ubon Rajathanee University, Ubon Ratchathani 34190, Thailand

Received 28 June 2005; Accepted 13 September 2005

Copyright © 2006 Weerayuth Nilsrakoo and Satit Saejung. 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 introduce a new class of normalized norms on ℝ2 which properly contains all absolute normalized norms. We also give a criterion for deciding whether a given norm in this class is uniformly nonsquare. Moreover, an estimate for the James constant is presented and the exact value of some certain norms is computed. This gives a partial answer to the question raised by Kato et al.