Nonlinear ergodic theorems for general curves defined on general semigroups

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• 作者：Li ; Gang ; Kim ; Jong Kyu
• 关键词：47H09 ; 47H10 ; 47H20 ; Nonlinear ergodic theorem ; Non-Lipschitzian mappings ; Almost-orbit ; Semitopological semigroup ; Asymptotically nonexpansive-type curve
• 刊名：Nonlinear Analysis
• 出版年：2003
• 期刊代码：43_0362546x
• 类别：mt
• 出版时间：October, 2003
• 卷：55
• 期：1-2
• 页码：1-14
• 文件大小：136 K

摘要

Let G be a (algebra) semigroup and let H be a real Hilbert space. Let F(G) be a set of all mappings from G into H. In this paper, we first try to provide a nonlinear ergodic retraction theorem for the mappings from G to H. Moreover, we introduce the notion of asymptotically nonexpansive-type curves and give the ergodic convergence theorems for this kind of curves. Using the main results, we can also prove the ergodic convergence theorem for the almost-orbits of semitopological semigroups of non-Lipschitzian mappings without convexity.