Hilbert空间中非Lipschitz连续半群的几乎轨道的渐近行为  

ASYMPTOTIC BEHAVIOR OF ALMOST-ORBITS OF NON-LIPSCHITZIAN CONTINUOUS SEMIGROUPS IN HILBERT SPACES

作　　者：曾六川[1] 

机构地区：[1]上海师范大学数学系,上海200234

出　　处：《数学杂志》2005年第4期405-412,共8页Journal of Mathematics

基　　金：国家教育部高等学校优秀青年教师教学和科研奖励基金资助的项目;上海市教委重点学科经费(部分)资助的项目;上海市曙光计划基金资助的项目

摘　　要：本文研究{u(t)}的渐近行为.证明了{u(t)}几乎弱收敛到集∩S≥0co{u(t)t≥s}∩F(T)的唯一点.利用该结果,推得,{u(t)}弱收敛到T的不动点,当且仅当对每个h≥0,当t→∞时{u(t+h)-u(t)}弱收敛到零向量.The purpose of this paper is to investigate the asymptotic behavior of {u(t)}. It is shown that {u(t)} almost converges weakly to the unique point of the set ∩s≥0 co {u(t):t≥s}∩F(T). It follows immediately from this result that {u(t)} converges weakly to a fixed point of T if and only if {u(t+h)- u(t)} converges weakly to zero as t tends to infinity for each h≥0.

关 键 词：几乎轨道 近似渐近非扩张型半群 不动点 渐近行为 距离投影 

分 类 号：O177.91[理学—数学]