Banach空间上非Lipschitz映射的渐近行为(英文).pdf

Journal of Mathematical Research Exposition Vol. 18 , No. 3 , 319 - 325 , August 1998 Asymptotic Behavior of Non - Lipschitzian Ma ppings in Banach Spaces L i Gang (Dept . of Math. , Yangzhou Univ. , Yangzhou 225002) Abstract 　Let C be a nonempt y bounded closed convex subset of a uniformly convex Banach space with a Fréchet differentiable norm , and G be a directed system , let T = { Tt : t ∈G} be asymptotically non expansive t ype mappings on C . We give the weak convergence theorem of { Tt : t ∈G} in this paper. Keywords 　directed system , asymptotica behavior , asymptotically nonexpansive t ype map pings. Classif ication 　AMS ( 1991) 47H09/ CCL O152. 7 1. Introduction and Preliminary Let E be a uniformly convex Banach space , and C be a closed convex subset of E . The sequence { T } ∞ of self - mappings of C is said to be asymptotically nonexpansive ( Passty[ 5 ]) if ‖T x - n n = 1 n T y ‖≤K ‖x - y ‖for all x ,y in C with lim K = 1 . n n n →∞ n Feathers and Dotson[ 3] and Bose[ 1] gave the weak convergence theorem of asymptotically nonex pansive mappings in a uniformly convex Banach space with weak continous duality mapping by using Opial ’s Lemma[ 4] . Using Bruck ’s Lemma[ 2] , Passty[ 5] extended the results of [ 1 ,3 ] to uniformly convex Banach sp