tailieunhanh - Báo cáo hóa học: " Semistability of iterations in cone spaces"

Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí sinh học đề tài :Semistability of iterations in cone spaces | Yadegarnegad et al. Fixed Point Theory and Applications 2011 2011 70 http content 2011 1 70 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access Semistability of iterations in cone spaces A Yadegarnegad 1 S Jahedi2 B Yousefi1 and SM Vaezpour3 Correspondence jahedi@sutech. 2Department of Mathematics Shiraz University of Technology P. O. Box 71555-313 Shiraz Iran Full list of author information is available at the end of the article Springer Abstract The aim of this work is to prove some iteration procedures in cone metric spaces. This extends some recent results of T-stability. Mathematics Subject Classification 47J25 26A18. Keywords Cone metric contraction stability nonexpansive affine semi-compact 1. Introduction Let E be a real Banach space. A subset P c E is called a cone in E if it satisfies in the following conditions i P is closed nonempty and P 0 . ii a b e R a b 0 and x y e P imply that ax by e P. iii x e P and -x e P imply that x 0. The space E can be partially ordered by the cone P c E by defining x y if and only if y - x e P Also we write x y if y - x e int P where int P denotes the interior of P. A cone P is called normal if there exists a constant k 1 such that 0 x y implies x k y . In the following we suppose that E is a real Banach space P is a cone in E and is a partial ordering with respect to P. Definition . 1 Let X be a nonempty set. Assume that the mapping d X X X E satisfies in the following conditions i 0 d x y for all x y e X and d x y 0 if and only if x y ii d x y d y x for all x y e X. iii d x y d x z d z y for all x y z e X. Then d is called a cone metric on X and X d is called a cone metric space. If T is a self-map of X then by F T we mean the set of fixed points of T. Also No denotes the set of nonnegative integers . No N u 0 . Definition . 2 If 0 a 1 0 b Y 1 we say that a map T X X is Zamfirescu with respect to a b g if for each pair x y e X T satisfies .