ITERATIVE APPROXIMATION OF FIXED POINTS OF (ASYMPTOTICALLY) NONEXPANSIVE MAPPINGS  

作　　者：Zeng LuchuanDept. of Math.,Shanghai Normal Univ.,Shanghai 200234. 

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2001年第4期402-408,共7页高校应用数学学报（英文版）（B辑）

基　　金：Supported both by the National Natural Science Foundation(1 980 1 0 2 3 ) and the Teaching and ResearchAward Fund for Outstanding Young Teachers in Higher Education Institutions of MOE;P.R.C

摘　　要：Let E be a uniformly convex Banach space which satisfies Opial's condition or has a Frechet differentiable norm,and C be a bounded closed convex subset of E. If T∶C→C is (asymptotically)nonexpansive,then the modified Ishikawa iteration process defined byx n+1 =t nT ns nT nx n+1-s nx n+(1-t n)x n,converges weakly to a fixed point of T ,where {t n} and {s n} are sequences in [0,1] with some restrictions.Let E be a uniformly convex Banach space which satisfies Opial's condition or has a Frechet differentiable norm,and C be a bounded closed convex subset of E. If T∶C→C is (asymptotically)nonexpansive,then the modified Ishikawa iteration process defined byx n+1 =t nT ns nT nx n+1-s nx n+(1-t n)x n,converges weakly to a fixed point of T ,where {t n} and {s n} are sequences in [0,1] with some restrictions.

关 键 词：Fixed point (asymptotically)nonexpansive mapping modified Ishikawa iteration process Frechet differentiable norm Opial condition. 

分 类 号：O177.2[理学—数学]