Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 676373, 15 pages
doi:10.1155/2009/676373
Research Article

Some Modulus and Normal Structure in Banach Space

Zhanfei Zuo and Yunan Cui

Department of Mathematics, Harbin University of Science and Technology, Harbin, Heilongjiang 150080, China

Received 29 September 2008; Revised 1 January 2009; Accepted 3 March 2009

Academic Editor: Jong Kim

Copyright © 2009 Zhanfei Zuo and Yunan Cui. 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.

Abstract

We present some sufficient conditions for which a Banach space X has normal structure in terms of the modulus of U-convexity, modulus of W∗-convexity, and the coefficient R(1,X), 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.