一致光滑Banach空间中φ-半压缩映象不动点的Noor迭代逼近  

Noor Iterative Approximation of Fixed Points for φ-Hemicontrative Mappings in Uniformly Smooth Banach Spaces

作　　者：赵亚莉 

机构地区：[1]朝阳师范专科学校，辽宁 朝阳 122000

出　　处：《常州工学院学报》2001年第4期5-8,共4页Journal of Changzhou Institute of Technology

摘　　要：设X是实一致光滑Banach空间,K是X的非空凸有界子集,T:K→K是φ-半压缩映象。{α_n}n≥0,{β_n}n≥0,{γ_n}n≥0是[0,1]中的实数列满足如下条件: ①α_n→0,β_n→0,γ_n→0(n→∞) ②sum from n=0 α_n(1-α_n)=∞ 则对任意的x_0∈K,由Noor迭代过程 z_n=(1-γ_n)x_n+γ_nTx_n,y_n=(1-β_n)x_n+β_nTz,x_(n+1)=(1-α_n)x_n+α_nTy_n,n≥0所产生的序列{x_n}n≥0,强收敛于T的唯一不动点。相关结果处理了关于φ-强拟增生算子的非线性方程的迭代解。Let X be a real uniformly smooth Banach space, K(?)X a nonempty convex and boundedsubset,T: K→K a (?) -hemicontraction. Let {αn}n≥0, {βn }n≥0, and {γn}n≥0 be real sequences in [0,1] satisfying the following conditions : Then, for arbitrary initial value x0∈K, the Noor iterative process {xn}n≥0generated by (N)converges strongly to the unique fixed point of T. A related result deals with the iterative solutions of nonlinear equations involving (?) -strongly quasi-accretive operators.

关 键 词：ψ-半压缩映象 Noor近代过程 Reich's不等式 一致光滑BANACH空间 不动点 Noor迭代逼近 

分 类 号：O177.91[理学—数学]