Table of Contents
ISRN Mathematical Analysis
Volume 2011, Article ID 514184, 5 pages
Research Article

Another Aspect of Triangle Inequality

1Department of Mathematics, Faculty of Science, Niigata University, Niigata 950-2181, Japan
2Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China
3Department of Mathematics and Information Science, Graduate School of Science and Technology, Niigata University, Niigata 950-2181, Japan
4Department of Systems Engineering, Okayama Prefectural University, Soja, Okayama 719-1197, Japan

Received 18 February 2011; Accepted 14 March 2011

Academic Editors: Y. Dai and B. Djafari-Rouhani

Copyright Β© 2011 Kichi-Suke Saito et al. 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.


We introduce the notion of πœ“ -norm by considering the fact that an absolute normalized norm on β„‚ 2 corresponds to a continuous convex function πœ“ on the unit interval [ 0 , 1 ] with some conditions. This is a generalization of the notion of π‘ž -norm introduced by Belbachir et al. (2006). Then we show that a πœ“ -norm is a norm in the usual sense.