tailieunhanh - báo cáo hóa học:" Research Article Relation between Fixed Point and Asymptotical Center of Nonexpansive Maps"

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 Relation between Fixed Point and Asymptotical Center of Nonexpansive Maps | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 175989 6 pages doi 2011 175989 Research Article Relation between Fixed Point and Asymptotical Center of Nonexpansive Maps Mohammad Reza Haddadi Hamid Mazaheri and Mohammad Hussein Labbaf Ghasemi Department of Mathematics Faculty of Mathematics Yazd University P. O. Box 89195-741 Yazd Iran Correspondence should be addressed to Mohammad Reza Haddadi haddadi83@ Received 19 October 2010 Accepted 22 November 2010 Academic Editor Qamrul Hasan Ansari Copyright 2011 Mohammad Reza Haddadi et al. 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 introduce the concept of asymptotic center of maps and consider relation between asymptotic center and fixed point of nonexpansive maps in a Banach space. 1. Introduction Many topics and techniques regarding asymptotic centers and asymptotic radius were studied by Edelstein 1 Bose and Laskar 2 Downing and Kirk 3 Goebel and Kirk 4 and Lan and Webb 5 . Now We recall that definitions of asymptotic center and asymptotic radius. Let C be a nonempty subset of a Banach space X and xn a bounded sequence in X. Consider the functional ra - xn X R defined by ra x xn limsupix - x x e X. n The infimum of ra xn over C is said to be the asymptotic radius of xn with respect to C and is denoted by ra C xn . A point z e C is said to be an asymptotic center of the sequence xn with respect to C if Ta z xn inf ra x xn x e C . The set of all asymptotic centers of xn with respect to C is denoted by Za C xn . 2 Fixed Point Theory and Applications We present new definitions of asymptotic center and asymptotic radius that is for a mapping and obtain new results. Definition . Let C be a bounded closed convex subset of X. A sequence xn c X is said to be an asymptotic center for a