Skip to content


  • Research Article
  • Open Access

Nonlinear Mean Ergodic Theorems for Semigroups in Hilbert Spaces

Fixed Point Theory and Applications20072007:073246

Received: 26 December 2006

Accepted: 4 April 2007

Published: 31 May 2007


Let be a nonempty subset (not necessarily closed and convex) of a Hilbert space and let be a semigroup on and let be an almost orbit of . In this paper, we prove that every almost orbit of is almost weakly and strongly convergent to its asymptotic center.


  • Hilbert Space
  • Differential Geometry
  • Computational Biology
  • Ergodic Theorem


Authors’ Affiliations

Department of Mathematics, Arts and Science Faculty, Harran University, Sanliurfa, Turkey


  1. Miyadera I: Nonlinear ergodic theorems for semigroups of non-Lipschitzian mappings in Hilbert spaces. Taiwanese Journal of Mathematics 2000,4(2):261–274.MathSciNetMATHGoogle Scholar
  2. Xu H-K: Strong asymptotic behavior of almost-orbits of nonlinear semigroups. Nonlinear Analysis 2001,46(1):135–151. 10.1016/S0362-546X(99)00453-8MathSciNetView ArticleMATHGoogle Scholar
  3. Takahashi W: A nonlinear ergodic theorem for an amenable semigroup of nonexpansive mappings in a Hilbert space. Proceedings of the American Mathematical Society 1981,81(2):253–256. 10.1090/S0002-9939-1981-0593468-XMathSciNetView ArticleMATHGoogle Scholar
  4. Kada O, Takahashi W: Strong convergence and nonlinear ergodic theorems for commutative semigroups of nonexpansive mappings. Nonlinear Analysis 1997,28(3):495–511. 10.1016/0362-546X(95)00161-NMathSciNetView ArticleMATHGoogle Scholar
  5. Oka H: Nonlinear ergodic theorems for commutative semigroups of asymptotically nonexpansive mappings. Nonlinear Analysis 1992,18(7):619–635. 10.1016/0362-546X(92)90002-VMathSciNetView ArticleMATHGoogle Scholar
  6. Wittmann R: Mean ergodic theorems for nonlinear operators. Proceedings of the American Mathematical Society 1990,108(3):781–788. 10.1090/S0002-9939-1990-1004427-2MathSciNetView ArticleMATHGoogle Scholar
  7. Miyadera I: Nonlinear mean ergodic theorems. Taiwanese Journal of Mathematics 1997,1(4):433–449.MathSciNetMATHGoogle Scholar
  8. Miyadera I: Nonlinear mean ergodic theorems—II. Taiwanese Journal of Mathematics 1999,3(1):107–114.MathSciNetMATHGoogle Scholar


© S. Temir and O. Gul. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.