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 l...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.展开更多
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.
文摘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.
基金Supported by the Natural Science Foundation of China(10971182)the Natural Science Foundation of Jiangsu Province(BK2010309 and BK2009179)+2 种基金the Tianyuan Youth Foundation(11026115)the Natural Science Foundation of Jiangsu Education Committee(10KJB110012) the Natural Science Foundation of Yangzhou University(2010CXJ003,2011CXJ001 and 2011CXJ002)
