一致L-Lipschitz的渐近伪压缩非自映象不动点的迭代逼近  

Itrative Approximation of Fixed Points of Uniformly L-Lipschitzian Asymptotically Pseudocontractive Nonself-mappings

作　　者：张芳[1] 向长合[1] 

机构地区：[1]重庆师范大学数学与计算机科学学院,重庆400047

出　　处：《重庆师范大学学报（自然科学版）》2009年第1期7-10,共4页Journal of Chongqing Normal University:Natural Science

基　　金：重庆市教委项目(No.KJ070806)

摘　　要：Chidume首次提出渐近非扩张非自映象、一致L-Lipschitz非自映象的定义,并证明了所引入的迭代序列强收敛于渐近非扩张非自映象的不动点。该文引入渐近伪压缩非自映象的概念,并对一致L-Lipschitz的渐近伪压缩非自映象T提出了具误差的修改的Ishikawa迭代序列{xn}。设K是实Banach空间E的收缩核,P是从E到K上的非扩张的收缩映象。若存在严格增加函数:[0,∞)→[0,∞),Φ(0)=0,j(xn+1-x*)∈J(xn+1-x*)使得〈T(PT)n-1xn+1-T(PT)n-1x*,j(xn+1-x*)〉≤kn‖xn+1-x*‖2-Φ(‖xn+1-x*‖),n≥1,x*是T的不动点,在对参数的一些限制条件下,本文证明了迭代序列{xn}强收敛于非自映象T的不动点x*,其目的是把对渐近伪压缩映象的迭代结果推广到渐近伪压缩非自映象上,从而推广了以前的结果。In 2003, Chidume first introduced the definition of asymptotically nonexpansive nonself-mappings and uniformly L- Lipschitzian nonself-mappings. Furthermore, he proved that the iterative sequence he introduced converged strongly to fixed point of asymptotically nonexpansive nonself-mappings. The definition of asymptotically pseudoeontraetive nonself-mapping is introduced and the modified Ishikawa iterative sequence {xn} for uniformly L-Lipschitzian asymptotically pseudoeontractive nonself-mapping T is presented in this paper. Let K be a retract of a real Banach space E, P be a nonexpansive retraction from E to K. Suppose there exist a strictly increasing function φ：[0,∞）→[0,∞）,φ（0）=0,E←j（xa＋1-x^＊）∈J（xn＋1-x^＊） such that （T（PT）^n＋1xa＋1-T（PT）^n-1x^＊,j（xa＋1-x^＊））≤kn｜｜xn＋1-x^＊｜｜^2-φ（｜｜xn＋1-x^＊｜｜,A↓n≥1,x^＊ is a fixed point of T. This paper proves that the iterative sequence { xn} converges strongly to fixed points x^＊ under some restrictive conditions on parameters. The objective of this article is to extend the asymptotically pseudocontraetive mappings to asymptotically pseudocontractive nonself-mappings. Therefore, the results presented in this paper extended the previous work.

关 键 词：一致L-Lipschite非自映象 渐近伪压缩非自映象 迭代序列 不动点 

分 类 号：O177.91[理学—数学]