Banach空间中的非Lipschitzian一般半群的非线性遍历定理(英文)  

NONLINEAR ERGODIC THEOREMS FOR GENERAL SEMIGROUPS OF NON-LIPSCHITZIAN MAPPINGS IN BANACH SPACES

作　　者：朱兰萍[1] 黄强联[1] 李刚[1] 

机构地区：[1]扬州大学数学科学学院,扬州225002

出　　处：《南京大学学报（数学半年刊）》2011年第2期176-186,共11页Journal of Nanjing University(Mathematical Biquarterly)

基　　金：Supported by the Natural Science Foundation of China(10971182);the Natural Science Foundation of Jiangsu Province(BK2010309 and BK2009179);the Tianyuan Youth Foundation(11026115);the Natural Science Foundation of Jiangsu Education Committee(10KJB110012) ;the Natural Science Foundation of Yangzhou University(2010CXJ003,2011CXJ001 and 2011CXJ002)

摘　　要：设G为半群,C为具FrEchet可微范数的一致凸Banach空间X的非空有界闭凸子集.(■)={T_t:t∈G}为C上到自身的渐近非扩张型半群,且F(■)非空.在本文中,我们证明了:对■的任一殆轨道u(·),■co{u(ts),t∈G}∩F(S)至多为单点集.进一步,对x∈C,∩_(s∈G)co{T_(ts)x,t∈G}∩F(■)非空当且仅当存在C到F(■)上非扩张压缩P,使得对任意t∈G,PT_t=T_tP=P,Px∈co{T_tx,t∈G}.这一结果不仅推广了许多已知结果,而且说明它们中的一些关键条件是不必要的.Abstract Let G be a semigroup. Let C be a nonempty bounded closed convex subset of a uniformly convex Banach space X with a Fr@chet differentiable norm and = {T_t：t∈G} be a semigroup of asymptotically nonexpansive type mappings on C with Fco{u（ts）,t∈G}. We prove in this paper that for every almost orbit u（-） of S, NsEc do co{u（ts）,t∈G}∩F（S） consists of at most one point. Fhrther, [S]sEG do{Ttsx, t C G} N F（S） is nonempty for each x C C if and only if there exists a nonexpansive retraction P of C onto F（~） such that PTt =TtP = P for all t E G and Px E Co{Ttx, t C G}. This result not only gengneralizes some well-known theorems, but also shows that some key conditions in them are not necessary.

关 键 词：非线性遍历定理 半群 渐近非扩张型映射 殆轨道 

分 类 号：O177.2[理学—数学]