|
An ergodic theorem for asymptotically nonexpansive mappings in the intermediate sense
Author(s):
Hirokazu
Oka
Journal:
Proc. Amer. Math. Soc.
125
(1997),
1693-1703.
MSC (1991):
Primary 47H09, 47H10
MathSciNet review:
1371136
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
This paper is concerned with an ergodic theorem for asymptotically nonexpansive mappings in the intermediate sense in Banach spaces.
References:
- 1.
- J.B. BAILLON, Un théorème de type ergodique pour les contractions non linéaires dans un espace de Hilbert, C. R. Acad. Sci. Paris Sér. A 280 (1975), 1511-1514. MR 51:11205
- 2.
- R.E. BRUCK, A simple proof of the mean ergodic theorem for nonlinear contractions in Banach spaces, Israel J. Math. 32 (1979), 107-116. MR 80j:47066
- 3.
- R.E. BRUCK, On the convex approximation property and the asymptotic behavior of nonlinear contractions in Banach spaces, Israel J. Math. 38 (1981), 304-314. MR 82h:47051
- 4.
- R.E. BRUCK, T. KUCZUMOW AND S. REICH, Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property, Colloq. Math. LXV (1993), 169-179. MR 94h:47106
- 5.
- K. GOEBEL AND W.A. KIRK, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 35 (1972), 171-174. MR 45:7552
- 6.
- W.A. KIRK, Fixed point theorems for non-Lipschitzian mappings of asymptotically nonexpansive type, Israel J. Math. 17 (1974), 339-346. MR 49:11330
- 7.
- I. MIYADERA AND K. KOBAYASI, On the asymptotic behaviour of almost-orbits of nonlinear contraction semigroups in Banach spaces, Nonlinear Analysis 6 (1982), 349-365. MR 84c:47064
- 8.
- H. OKA, A nonlinear ergodic theorem for asymptotically nonexpansive mappings in Banach spaces, Proc. Japan Acad. 65 (1989), 284-287. MR 91c:47115
- 9.
- H. OKA, On the nonlinear mean ergodic theorems for asymptotically nonexpansive mappings in Banach spaces, Public. Res. Inst. Math. Sci. (Kokyûroku) 730 (1990), 1-20.
- 10.
- H. OKA, Nonlinear ergodic theorems for commutative semigroups of asymptotically nonexpansive mappings, Nonlinear Analysis 18 (1992), 619-635. MR 93d:47126
- 11.
- S. REICH, Almost convergence and nonlinear ergodic theorems, J. Approx. Theory 24 (1978), 269-272. MR 80b:47079
- 12.
- S. REICH, Nonlinear ergodic theory in Banach spaces, Argonne National Laboratory Report No.79-69 (1979).
- 13.
- S. REICH, Weak convergence theorems for nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 67 (1979), 274-276. MR 80d:47090
- 14.
- S. REICH AND H.K. XU, Nonlinear ergodic theory for semigroups of Lipschitzian mappings, Comm. Appl. Nonlinear Analysis 1 (1994), 47-60. MR 95k:47099
- 15.
- K.K. TAN AND H.K. XU, The nonlinear ergodic theorem for asymptotically nonexpansive mappings in Banach space, Proc. Amer. Math. Soc. 114 (1992), 399-404. MR 92e:47100
- 16.
- K.K. TAN AND H.K. XU, A nonlinear ergodic theorem for asymptotically nonexpansive mappings, Bull. Austral. Math. Soc. 45 (1992), 25-36. MR 93c:47068
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (1991):
47H09, 47H10
Retrieve articles in all Journals with
MSC (1991):
47H09, 47H10
Additional Information:
Hirokazu
Oka
Affiliation:
School of Education, Department of Mathematics, Waseda University, 1-6-1 Nishi-Waseda, Shinjuku-ku, Tokyo 169-50, Japan
Address at time of publication:
Faculty of Engineering, Ibaraki University, 12-1 Nakanarusawa 4 chome, Hitachi, Ibaraki 316, Japan
Email:
oka@base.ibaraki.ac.jp
DOI:
10.1090/S0002-9939-97-03745-3
PII:
S 0002-9939(97)03745-3
Keywords:
Asymptotically nonexpansive mapping in the intermediate sense,
almost-orbit,
weak almost convergence,
convex approximation property
Communicated by:
Palle E. T. Jorgensen
Copyright of article:
Copyright
1997,
American Mathematical Society
|
