Strong convergence theorems for nonexpansive semi-groups in Banach spaces
Some strong convergence theorems of explicit composite iteration scheme for nonexpansive semi-groups in the framework of Banach spaces are established. Results presented in the paper not only extend and improve the corresponding results of Shioji-Takahashi, Suzuki, Xu and Aleyner-Reich, but also give a partially affirmative answer to the open questions raised by Suzuki and Xu.
Key wordsnonexpansive semi-group demi-closed principle common fixed point uniformly smooth Banach space weakly continuous normalized duality mapping
Chinese Library ClassificationO177.91
2000 Mathematics Subject Classification47H20 47H10
Unable to display preview. Download preview PDF.
- Goebel K, Kirk W A. Topics in metric fixed point theory[M]. In: Cambridge Studies in Advanced Mathematics, Cambridge: Cambridge Univ Press, 1990.Google Scholar
- Barbu V. Nonlinear semi-groups and differential equations in Banach spaces[M]. Noordhoff, 1976.Google Scholar
- Goebel K, Reich S. Uniform convexity, hyperbolic geometry and nonexpansive mappings[M]. In: Monographs and Textbooks in Pure and Applied Mathematics, New York: Marcel Dekker Inc, 1984.Google Scholar