ON THE EXISTENCE OF FIXED POINTS FOR MAPPINGS OF ASYMPTOTICALLY NONEXPANSIVE TYPE  

作　　者：ZENGLuchuan 

机构地区：[1]DepartmentofMathematics,ShanghaiNormalUniversity,Shanghai200234,China

出　　处：《Journal of Systems Science & Complexity》2004年第2期188-196,共9页系统科学与复杂性学报（英文版）

基　　金：This research is supported both by the Teaching ; Research Award Fund tor Outstanding Young Teachers in Higher Education Institutions of MOE, P. R. C., ;by the Dawn Program Fund in Shanghai.

摘　　要：Let C be a nonempty weakly compact convex subset of a Banach space X, and T : C →C a mapping of asymptotically nonexpansive type. Then there hold the following conclusions: (i) if X has uniform normal structure and limsup |||TjN||| < N(X)~1/(N(X)) , where|||TjN||| is the exact Lipschitz constant of TjN , N is some positive integer, and N(X) is the normal structure coefficient of X, then T has a fixed point; (ii) if X is uniformly convex in every direction and has weak uniform normal structure, then T has a fixed point.

关 键 词：Mapping of asymptotically nonexpansive type fixed point uniform normal structure weak uniform normal structure uniform convexity in every direction. 

分 类 号：O177.91[理学—数学]