τ是X的一个线性H ausdorff拓扑,在一致τ-O p ia l或τ-UKK条件下,给出了渐近非扩张型映照的不动点定理.由于L1(μ)并不具备通常的O p ia l条件,但是在L1(μ)赋予抽象测度拓扑τ下,(X,τ)满足一致τ-O p ia条l件,从而给出L1(μ)中渐近...τ是X的一个线性H ausdorff拓扑,在一致τ-O p ia l或τ-UKK条件下,给出了渐近非扩张型映照的不动点定理.由于L1(μ)并不具备通常的O p ia l条件,但是在L1(μ)赋予抽象测度拓扑τ下,(X,τ)满足一致τ-O p ia条l件,从而给出L1(μ)中渐近非扩张型映照的不动点定理.展开更多
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
文摘τ是X的一个线性H ausdorff拓扑,在一致τ-O p ia l或τ-UKK条件下,给出了渐近非扩张型映照的不动点定理.由于L1(μ)并不具备通常的O p ia l条件,但是在L1(μ)赋予抽象测度拓扑τ下,(X,τ)满足一致τ-O p ia条l件,从而给出L1(μ)中渐近非扩张型映照的不动点定理.
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.
