渐近非扩张型映射的不动点迭代和△-收敛定理  

Fixed-Point Iterations and △-Convergence Theorem for Mappings of Asymptotically Nonexpansive Type

作　　者：左占飞[1] 

机构地区：[1]重庆三峡学院数学与统计学院,万州404100

出　　处：《数学学报（中文版）》2014年第2期387-394,共8页Acta Mathematica Sinica：Chinese Series

基　　金：重庆市教委科学技术研究项目资助(KJ131104)

摘　　要：研究了一致凸双曲度量空间中渐近非扩张型映射的三步迭代,这种迭代包括了Ishikawa型迭代和Krasnoselski-Mann迭代作为特例.作为应用还得到了迭代算法在CAT(0)空间中的△-收敛定理,得到的结论推广并加强了以前的许多已知结果.We analyze a three-step iterative scheme for mappings of asymptotically nonexpansive type in uniformly convex hyperbolic spaces. The new iterative scheme includes Ishikawa-type and Krasnoselski-Mann iteration as special cases. As an ap plication, we obtain a △-convergence theorem of the three-step iterative scheme for mappings of asymptotically nonexpansive type in CAT（0） spaces. The results obtained in this paper represent an extension as well as refinement of previous known results.

关 键 词：三步迭代 渐近非扩张型映射 一致凸双曲度量空闻△-收敛定理 CAT(O) 空间 

分 类 号：O177.91[理学—数学]