Construction of fixed points for asymptotically nonexpansive mappings
HTML articles powered by AMS MathViewer
- by Gregory B. Passty PDF
- Proc. Amer. Math. Soc. 84 (1982), 212-216 Request permission
Abstract:
In uniformly convex Banach spaces with Fréchet differentiable norms (e.g. ${L^p}$, $1 < p < \infty$), fixed points for asymptotically nonexpansive mappings are constructed as weak limits of iterates of the mappings themselves or of related mappings.References
-
J. B. Baillon, Thèse, Université de Paris.
- S. C. Bose, Weak convergence to the fixed point of an asymptotically nonexpansive map, Proc. Amer. Math. Soc. 68 (1978), no. 3, 305–308. MR 493543, DOI 10.1090/S0002-9939-1978-0493543-4
- Felix E. Browder, Nonlinear operators and nonlinear equations of evolution in Banach spaces, Nonlinear functional analysis (Proc. Sympos. Pure Math., Vol. XVIII, Part 2, Chicago, Ill., 1968) Amer. Math. Soc., Providence, R.I., 1976, pp. 1–308. MR 0405188
- Ronald E. Bruck, A simple proof of the mean ergodic theorem for nonlinear contractions in Banach spaces, Israel J. Math. 32 (1979), no. 2-3, 107–116. MR 531254, DOI 10.1007/BF02764907
- G. Feathers, J. Wayne Pace, and W. G. Dotson Jr., A nonlinear theorem of ergodic type, Proc. Amer. Math. Soc. 73 (1979), no. 1, 35–36. MR 512053, DOI 10.1090/S0002-9939-1979-0512053-X
- K. Goebel and W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 35 (1972), 171–174. MR 298500, DOI 10.1090/S0002-9939-1972-0298500-3
- Zdzisław Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967), 591–597. MR 211301, DOI 10.1090/S0002-9904-1967-11761-0
- Helmut Schaefer, Über die Methode sukzessiver Approximationen, Jber. Deutsch. Math.-Verein. 59 (1957), no. Abt. 1, 131–140 (German). MR 84116
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 84 (1982), 212-216
- MSC: Primary 47H10
- DOI: https://doi.org/10.1090/S0002-9939-1982-0637171-7
- MathSciNet review: 637171