期刊信息
- 刊名： 河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
- 主办： 河北师范大学
- ISSN： 1000-5854
- CN： 13-1061/N
- 中国科技核心期刊
- 中国期刊方阵入选期刊
- 中国高校优秀科技期刊
- 华北优秀期刊
- 河北省优秀科技期刊
Ishikawa Iteration Convergence Theorems for Nonexpansive Mappings when Parameter Approximate End Point of [0,1]
摘要/Abstract
摘要：
设X是一致凸Banach空间,C是X中非空闭凸子集,T:C→C是具不动点的非扩张映像,对任意的x1∈C,存在Ishikawa迭代过程{xn}(xn+1=(1-tn)xn+tnT(snTxn+(1-sn)xn.
Abstract：
Let X be a uniformly convex Banach space and C be a nonempty colsed convex subset of X,and T:C→C be a nonexpansive mapping,for x_1∈C and {s_n},{t_n}[0,1],exsits subsequence{x_(n_k)}of x_(n+1)=(1-t_n)x_n+t_nT(s_nTx_n+(1-s_n)x_n),t_n→1,s_n→0,∑∞n=1(1-t_n)=+∞, such that‖x_(n_k)-Tx_(n_k)‖→0(k→∞),if T is compact then Ishikawa iterative process {x_(n_k)}converges strongly to a fixed point,if X satisfies Opial's condition then Ishikawa iterative process {x_(n_k)}converges weakly to a fixed point.
关键词
Key words：
nonexpansive mapping
;
iteration process
;
fixed point
;
uniformly convex
;
convergence
;