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Some Properties of Pythagorean Modulus

Abstract

We consider two Pythagorean modulus introduced by Gao (2005, 2006) recently. The exact values concerning these modulus for some classical Banach spaces are determined. Some applications in geometry of Banach spaces are also obtained.

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References

  1. Gao J: Normal structure and Pythagorean approach in Banach spaces. Periodica Mathematica Hungarica 2005,51(2):19–30. 10.1007/s10998-005-0027-3

    MathSciNet  Article  MATH  Google Scholar 

  2. Gao J: A Pythagorean approach in Banach spaces. Journal of Inequalities and Applications 2006, 2006: 11 pages.

    Article  Google Scholar 

  3. Saejung S: On James and von Neumann-Jordan constants and sufficient conditions for the fixed point property. Journal of Mathematical Analysis and Applications 2006,323(2):1018–1024. 10.1016/j.jmaa.2005.11.005

    MathSciNet  Article  MATH  Google Scholar 

  4. Yang C, Wang F: On a new geometric constant related to the von Neumann-Jordan constant. Journal of Mathematical Analysis and Applications 2006,324(1):555–565. 10.1016/j.jmaa.2005.12.009

    MathSciNet  Article  MATH  Google Scholar 

  5. Clarkson JA: Uniformly convex spaces. Transactions of the American Mathematical Society 1936,40(3):396–414. 10.1090/S0002-9947-1936-1501880-4

    MathSciNet  Article  Google Scholar 

  6. Takahashi Y, Kato M: Clarkson and random Clarkson inequalities for. Mathematische Nachrichten 1997,188(1):341–348. 10.1002/mana.19971880118

    MathSciNet  Article  MATH  Google Scholar 

  7. Banaś J, Rzepka B: Functions related to convexity and smoothness of normed spaces. Rendiconti del Circolo Matematico di Palermo 1997,46(3):395–424. 10.1007/BF02844281

    MathSciNet  Article  MATH  Google Scholar 

  8. Milman VD: Infinite-dimensional geometry of the unit sphere in Banach space. Soviet Mathematics Doklady 1967, 8: 1440–1444.

    Google Scholar 

  9. Lindenstrauss J: On the modulus of smoothness and divergent series in Banach spaces. The Michigan Mathematical Journal 1963,10(3):241–252.

    MathSciNet  Article  Google Scholar 

  10. He C, Cui Y: Some properties concerning Milman's moduli. Journal of Mathematical Analysis and Applications 2007,329(2):1260–1272. 10.1016/j.jmaa.2006.07.046

    MathSciNet  Article  MATH  Google Scholar 

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Correspondence to Fenghui Wang.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Wang, F. Some Properties of Pythagorean Modulus. J Inequal Appl 2007, 071012 (2008). https://doi.org/10.1155/2007/71012

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  • DOI: https://doi.org/10.1155/2007/71012

Keywords

  • Banach Space
  • Classical Banach Space