Banach空间中非Lipschitzian非自身映射的一类迭代序列收敛定理  

Convergence Theorems for an Iteration of Non-Lipschitzian Nonself Mappings in Banach Spaces

作　　者：吴莉 杨红莉 WU Li;YANG Hongli(Department of Mathematics and Physics,Nanjing Institute of Technology,Nanjing 211167,China)

机构地区：[1]南京工程学院数理部,江苏南京211167

出　　处：《南通大学学报（自然科学版）》2021年第1期82-87,共6页Journal of Nantong University(Natural Science Edition)　

基　　金：国家自然科学基金项目(11701274)。

摘　　要：在一致凸Banach空间,对具有中间意义的渐近非扩张型非自身映射引入一类新的带误差迭代序列,并研究该迭代序列的收敛性。首先,证明若一致凸Banach空间X具有Opial条件或共轭空间X*具有Kadec-Klee(KK)性质,则映射存在不动点当且仅当迭代序列{x_(n)}弱收敛于x,且lim_(m→∞) lim sup_(m→∞)‖T(PT)^(m-1)xn-xn‖=0.;然后,在映射弱于完全连续的Browder-Petryshyn(BP)条件下,给出迭代序列的强收敛性定理。In this study,a new iteration with errors for non-Lipschitzian nonself mappings in the uniformly convex Banach space is introduced.The convergence of such iteration is investigated and which proves that if the uniformly convex Banach space X satisfies Opial′s condition or its dual space X*has the Kadec-Klee property,then F(T)is nonempty if and only if{x_(n)}converges weakly to x and lim_(m→∞) lim sup_(m→∞)‖T(PT)^(m-1)xn-xn‖=0.The strong convergence theorem under the condition Browder-Petryshyn(BP)which is strictly weak than the complete continuity is provided.

关 键 词：渐近非扩张型非自身映射 OPIAL条件 Kadec-Klee性质 Browder-Petryshyn条件 不动点 

分 类 号：O177.91[理学—数学]