Banach空间中渐近非扩张映射的收敛定理  

Convergence theorems for asymptotically nonexpansive mappings in Banach space

作　　者：吴莉[1] 

机构地区：[1]南京工程学院基础部

出　　处：《东南大学学报（自然科学版）》2003年第6期804-806,共3页Journal of Southeast University：Natural Science Edition

摘　　要：设X为具有Opial条件的一致凸Banach空间 ,C为X的非空有界闭凸子集 ,T ,S为C到自身的 2个渐近非扩张映射且T和S有公共的不动点 .本文主要考察了一种带误差的迭代逼近T和S有公共的不动点 ,在迭代参数 {an},{bn},{cn},{a′n},{b′n},{c′n}的适当假设下 ,证明了所构造的带误差的迭代序列弱收敛于T和S的某个公共不动点 。Let X be a uniform Banach space satisfying Opial condition and C a nonempty bounded closed convex subset of X . Let T, S be two asymptotically nonexpansive mappings on C with F(T)∩F(S)≠ . This paper deals with approximating common fixed point of T and S through an iterative sequence with errors. Under some suitable assumptions on the iteration parameters {a n}, {b n}, {c n}, {a′ n}, {b′ n} , an d {c′ n}, we have proved that the iterative sequence with errors converges weakly to some common fixed point of T and S . We also investigate the strong convergence of such iterative sequence.

关 键 词：渐近非扩张映射 一致凸BANACH空间 OPIAL条件 

分 类 号：O177.91[理学—数学]