Table of Contents
ISRN Mathematical Analysis
Volume 2011, Article ID 514184, 5 pages
http://dx.doi.org/10.5402/2011/514184
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 © 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.

Linked References

  1. M. Kato, K.-S. Saito, and T. Tamura, “Sharp triangle inequality and its reverse in Banach spaces,” Mathematical Inequalities & Applications, vol. 10, no. 2, pp. 451–460, 2007. View at Google Scholar · View at Zentralblatt MATH
  2. M. Fujii, M. Kato, K.-S. Saito, and T. Tamura, “Sharp mean triangle inequality,” Mathematical Inequalities & Applications, vol. 13, no. 4, pp. 743–752, 2010. View at Google Scholar
  3. K.-I. Mitani, K.-S. Saito, M. Kato, and T. Tamura, “On sharp triangle inequalities in Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 336, no. 2, pp. 1178–1186, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. K.-I. Mitani and K.-S. Saito, “On sharp triangle inequalities in Banach spaces II,” Journal of Inequalities and Applications, vol. 2010, Article ID 323609, 17 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. S. Saitoh, “Generalizations of the triangle inequality,” Journal of Inequalities in Pure and Applied Mathematics, vol. 4, no. 3, article 62, pp. 1–5, 2003. View at Google Scholar · View at Zentralblatt MATH
  6. H. Belbachir, M. Mirzavaziri, and M. S. Moslehian, “q-norms are really norms,” The Australian Journal of Mathematical Analysis and Applications, vol. 3, no. 1, article 2, pp. 1–3, 2006. View at Google Scholar · View at Zentralblatt MATH
  7. K.-S. Saito, M. Kato, and Y. Takahashi, “Von Neumann-Jordan constant of absolute normalized norms on 2,” Journal of Mathematical Analysis and Applications, vol. 244, no. 2, pp. 515–532, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. Y. Takahashi, M. Kato, and K.-S. Saito, “Strict convexity of absolute norms on 2 and direct sums of Banach spaces,” Journal of Inequalities and Applications, vol. 7, no. 2, pp. 179–186, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH