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

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.