APPROXIMATION OF FIXED POINTS OF STRICTLY PSEUDO-CONTRACTIVE MAPPING WITHOUT LIPSCHITZ ASSUMPTION  

作　　者：Huang ZhenyuDept. of Math.,Nanjing Univ.,Nanjing 210093. 

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2000年第1期73-77,共5页高校应用数学学报（英文版）（B辑）

摘　　要：Without the Lipschitz assumption and boundedness of K in arbitrary Banach spaces, the Ishikawa iteration ｛x n｝ ∞ n=1 defined byx 1∈K,\ x n+1 =(1-α n)x n+α nTy n,\ y n=(1-β n)x n+β nTx n,\ n≥1satisfying 0<α n,β n<1 ,for all n≥1;∑ ∞ n=1 α n=∞;α n→0,β n→0 as n→∞ is proved to converge strongly to the unique fixed point of T ,where T:K→K is a uniformly continuous strictly pseudo\|contractive operator with bounded range.Without the Lipschitz assumption and boundedness of K in arbitrary Banach spaces, the Ishikawa iteration ｛x n｝ ∞ n=1 defined byx 1∈K,\ x n+1 =(1-α n)x n+α nTy n,\ y n=(1-β n)x n+β nTx n,\ n≥1satisfying 0<α n,β n<1 ,for all n≥1;∑ ∞ n=1 α n=∞;α n→0,β n→0 as n→∞ is proved to converge strongly to the unique fixed point of T ,where T:K→K is a uniformly continuous strictly pseudo\|contractive operator with bounded range.

关 键 词：Strictly pseudo-contractive Ishikaw a iterative process arbitrary real Banach spaces uni- form ly continuous 

分 类 号：O177[理学—数学]