Nonlinear ergodic theorems for general curves defined on general semigroups

✍ Scribed by Gang Li; Jong Kyu Kim

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 136 KB
• Volume: 55
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/s0362-546x(03)00194-9

✦ Synopsis

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 ÿrst 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.