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Non-Archimedean Hudzik-Landes-Dragomir-Kato-Saito-Tamura Inequality

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Contributed by K. MAHESH KRISHNA ↗

Version 1 / Oct 13, 2026 / CC BY 4.0

Abstract

In 1992, Hudzik and Landes \textit{[Math. Ann.]} derived a breakthrough generalization of the triangle inequality for two nonzero elements in normed linear spaces, which was generalized to finitely many nonzero elements independently in 2006 by Dragomir \textit{[Bull. Aust. Math. Soc.]} and in 2007 by Kato, Saito and Tamura \textit{[Math. Inequal. Appl]}. We derive a non-Archimedean version of Hudzik-Landes-Dragomir-Kato-Saito-Tamura inequality.

References

  1. Sever S. Dragomir. Bounds for the normalised Jensen functional. Bull. Aust. Math. Soc. , 74(3):471--478, 2006.
  2. Henryk Hudzik and Thomas R. Landes. Characteristic of convexity of K ö the function spaces. Math. Ann. , 294(1):117--124, 1992.
  3. Mikio Kato, Kichi-Suke Saito, and Takayuki Tamura. Sharp triangle inequality and its reverse in Banach spaces. Math. Inequal. Appl. , 10(2):451--460, 2007.
  4. Lech Maligranda. Simple norm inequalities. Am. Math. Mon. , 113(3):256--260, 2006.
  5. C. Perez-Garcia and W. H. Schikhof. Locally convex spaces over non- Archimedean valued fields , volume 119 of Camb. Stud. Adv. Math. Cambridge: Cambridge University Press, 2010.
  6. W. H. Schikhof. Ultrametric calculus. An introduction to pp-adic analysis , volume 4 of Camb. Stud. Adv. Math. Cambridge: Cambridge University Press, 2006.

Version history

  1. v1Submitted by K. MAHESH KRISHNAInitial depositCurrentOct 13, 2026