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