The Approximation of Fixed Points of Compositions of Nonexpansive Mappings in Hilbert Space
关键词:
摘要: Determining fixed points of nonexpansive mappings is a frequent problem in mathematics and physical sciences. An algorithm for finding common Hilbert space, essentially due to Halpern, analyzed. The main theorem extends Wittmann's recent work partially generalizes result by Lions. Algorithms this kind have been applied the convex feasibility problem.
core.ac.uk
elsevier.com
sci-hub.se 参考文章(15)
P. L. Lions, Approximation de Points Fixes de Contractions C. R. Acad. Sci. Paris S'erie A-B. ,vol. 284, pp. 1357- 1359 ,(1977)
W. A. Kirk, Kazimierz Goebel, Topics in metric fixed point theory ,(1990)
Rainer Wittmann, Approximation of Fixed Points of Nonexpansive Mappings Archiv der Mathematik. ,vol. 58, pp. 486- 491 ,(1992) , 10.1007/BF01190119
Jonathan Borwein, Simeon Reich, Itai Shafrir, Krasnoselski-Mann Iterations in Normed Spaces Canadian Mathematical Bulletin. ,vol. 35, pp. 21- 28 ,(1992) , 10.4153/CMB-1992-003-0
P.L. Combettes, The foundations of set theoretic estimation Proceedings of the IEEE. ,vol. 81, pp. 182- 208 ,(1993) , 10.1109/5.214546
Heinz H. Bauschke, Jonathan M. Borwein, On Projection Algorithms for Solving Convex Feasibility Problems SIAM Review. ,vol. 38, pp. 367- 426 ,(1996) , 10.1137/S0036144593251710
R. Tyrrell Rockafellar, Monotone Operators and the Proximal Point Algorithm SIAM Journal on Control and Optimization. ,vol. 14, pp. 877- 898 ,(1976) , 10.1137/0314056
Benjamin Halpern, Fixed points of nonexpanding maps Bulletin of the American Mathematical Society. ,vol. 73, pp. 957- 961 ,(1967) , 10.1090/S0002-9904-1967-11864-0
H. H. Bauschke, J. M. Borwein, On the convergence of von Neumann's alternating projection algorithm for two sets Set-valued Analysis. ,vol. 1, pp. 185- 212 ,(1993) , 10.1007/BF01027691
Zdzisław Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings Bulletin of the American Mathematical Society. ,vol. 73, pp. 591- 597 ,(1967) , 10.1090/S0002-9904-1967-11761-0