- Research Article
- Open access
- Published:
Nonlinear Mean Ergodic Theorems for Semigroups in Hilbert Spaces
Fixed Point Theory and Applications volume 2007, Article number: 073246 (2007)
Abstract
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.
References
Miyadera I: Nonlinear ergodic theorems for semigroups of non-Lipschitzian mappings in Hilbert spaces. Taiwanese Journal of Mathematics 2000,4(2):261–274.
Xu H-K: Strong asymptotic behavior of almost-orbits of nonlinear semigroups. Nonlinear Analysis 2001,46(1):135–151. 10.1016/S0362-546X(99)00453-8
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-X
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-N
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-V
Wittmann R: Mean ergodic theorems for nonlinear operators. Proceedings of the American Mathematical Society 1990,108(3):781–788. 10.1090/S0002-9939-1990-1004427-2
Miyadera I: Nonlinear mean ergodic theorems. Taiwanese Journal of Mathematics 1997,1(4):433–449.
Miyadera I: Nonlinear mean ergodic theorems—II. Taiwanese Journal of Mathematics 1999,3(1):107–114.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Temir, S., Gul, O. Nonlinear Mean Ergodic Theorems for Semigroups in Hilbert Spaces. Fixed Point Theory Appl 2007, 073246 (2007). https://doi.org/10.1155/2007/73246
Received:
Accepted:
Published:
DOI: https://doi.org/10.1155/2007/73246