tailieunhanh - Báo cáo hóa học: " Research Article Some Modulus and Normal Structure in Banach Space"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Some Modulus and Normal Structure in Banach Space | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 676373 15 pages doi 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 Correspondence should be addressed to Zhanfei Zuo zuozhanfei@ Received 29 September 2008 Revised 1 January 2009 Accepted 3 March 2009 Recommended by Jong Kim 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. Copyright 2009 Z. Zuo and Y. 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. 1. Introduction We assume that X and X stand for a Banach space and its dual space respectively. By SX and BX we denote the unit sphere and the unit ball of a Banach space X respectively. Let C be a nonempty bounded closed convex subset of a Banach space X. A mapping T C C is said to be nonexpansive provided the inequality Tx - Ty x - yll holds for every x y e C. A Banach space X is said to have the fixed point property if every nonexpansive mapping T C C has a fixed point where C is a nonempty bounded closed convex subset of a Banach space X. Recall that a Banach space X is called to be uniformly nonsquare if there exists Ô 0 such that x yịị 2 1 - Ỗ or x - y 2 1 - Ỗ whenever x y e SX. A bounded convex subset K of a Banach space X is said to have normal structure if for every convex subset H 2 Journal of Inequalities and .