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: Convergence theorem for finite family of lipschitzian demi-contractive semigroups | Ali and Ugwunnadi Fixed Point Theory and Applications 2011 2011 18 http content 2011 1 18 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access Convergence theorem for finite family of lipschitzian demi-contractive semigroups Bashir Ali and Godwin Chidi Ugwunnadi i Correspondence bashiralik@ Department of Mathematical Sciences Bayero University Kano Nigeria SpringerOpen0 Abstract Let E be a real Banach space and K be a nonempty closed and convex subset of E. Let Jil j be a finite family of Lipschitzian demi-contractive semigroups of K with sequences of bounded measurable functions L - 0 0 and bounded functions li 0 0 respectively where Ji Ti t t 0 i 1 2 . N. Strong convergence theorem for common fixed point for finite family Ji l 1 is proved in a real Banch space. As an application a new convergence theorem for finite family of Lipschitzian demi-contractive maps is also proved. Mathematics subject classification 2000 47H09 47J25 Keywords Demi-contractive maps Demi-contractive semigroup Demicompact maps Fixed point 1. Introduction Let E be a real Banach space and E be the dual space of E. The normalized duality mapping J E 2E is defined by x e E Jx x e E xx x x x x where . . denotes the normalized duality pairing. For any x e E an element of Jx is denoted by j x . Let K be a nonempty closed and convex subset of E. Let T K K be a map a point x e K is called a fixed point of T if Tx x and the set of all fixed points of T is denoted by F T . The mapping T is called L-Lipschitzian or simply Lipschitz if 3L 0 such that Tx -Ty L x - y Vx y e K and if L 1 then the map T is called nonexpansive. A one parameter family J T t t 0 of self mapping of K is called a nonexpan-sive semigroup if the following conditions are satisfied i T 0 x x V x e K ii T t s T t T s V t s 0 iii for each x e K the mapping t T t x is continuos iv for x y e K and t 0 T t x -T t y x - y . If the family J T t t 0 satisfies .
