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Open Access

Some Modulus and Normal Structure in Banach Space

Journal of Inequalities and Applications20092009:676373

Received: 29 September 2008

Accepted: 3 March 2009

Published: 8 March 2009


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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Authors’ Affiliations

Department of Mathematics, Harbin University of Science and Technology, Harbin, China


© Z. Zuo and Y. Cui. 2009

This article is published under license to BioMed Central Ltd. 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.