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Some Modulus and Normal Structure in Banach Space

Abstract

We present some sufficient conditions for which a Banach space has normal structure in terms of the modulus of -convexity, modulus of -convexity, and the coefficient , which generalized some well-known results. Furthermore the relationship between modulus of convexity, modulus of smoothness, and Gao's constant is considered, meanwhile the exact value of Milman modulus has been obtained for some Banach space.

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Correspondence to Zhanfei Zuo.

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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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Zuo, Z., Cui, Y. Some Modulus and Normal Structure in Banach Space. J Inequal Appl 2009, 676373 (2009). https://doi.org/10.1155/2009/676373

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Keywords

  • Banach Space
  • Normal Structure
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