Banach空间中一类混合映射不动点的Ishikawa迭代逼近问题  

Ishikawa Iterative Approximation for Fixed Point with Mixed Mapping in Banach Spaces

作　　者：汪志明[1] 

机构地区：[1]唐山学院基础部,河北唐山063000

出　　处：《数学的实践与认识》2007年第9期180-183,共4页Mathematics in Practice and Theory

摘　　要：设E为一致光滑Banach空间,K为E的非空闭凸子集,T:K→K为Φ-强伪压缩映射.其中T=T1+T2,T1:K→K为Lipschitz映射,T2:K→K为具有有界值域映射.设{αn}n∞=0和{βn}n∞=0是[0,1]中满足一定条件的两实数列.则Ishikawa迭代序列{xn}∞n=0强收敛于T的唯一不动点.Suppose that E is an uniformly smooth real Banach space, and K is a nonempty closed convex subset of E,T：K→K is Ф-strongly pseudocontrictive mapping, and T=T1＋T2 ,T1 ：K→ K is Lipschitz mapping, T2：K→ K is a continuous mapping with the bounded range R（T）. Let {αn）∞ n=0 and {βn）∞ n=0 be two real sequences in [0, 1] satisfying suitable conditions, then Ishikawa iterative process {xn}∞ n=0 converges strongly to the unique fixed point of T.

关 键 词：LIPSCHITZ映射 有界值域映射 Ф-强伪压缩映射 ISHIKAWA迭代 一致光滑BANACH空间 

分 类 号：O177.2[理学—数学]