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ISSN 1088-6850(e) ISSN 0002-9947(p)

Path stability and nonlinear weak ergodic theorems

Author(s): Yong-Zhuo Chen
Journal: Trans. Amer. Math. Soc. 352 (2000), 5279-5292.
MSC (2000): Primary 47H07, 47H09; Secondary 47H10
Posted: July 12, 2000
MathSciNet review: 1707493
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Abstract | References | Similar articles | Additional information

Abstract: Let $\{f_{n} \}$ be a sequence of nonlinear operators. We discuss the asymptotic properties of their inhomogeneous iterates $f_{n} \circ f_{n-1} \circ \cdots \circ f_{1}\,$ in metric spaces, then apply the results to the ordered Banach spaces through projective metrics. Theorems on path stability and nonlinear weak ergodicity are obtained in this paper.

References:

1.: D. W. Boyd and J. S. W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc. 20(1969), 458-464. MR 39:916
2.: T. A. Burton, Integral equations, implicit functions and fixed points, Proc. Amer. Math. Soc. 124(1996), 2383-2390. MR 96j:45001
3.: Y.-Z. Chen, Thompson's metric and mixed monotone operators, J. Math. Anal. Appl. 117(1993), 31-37. MR 94d:47055
4.: Y.-Z. Chen, Inhomogeneous iterates of contraction mappings and nonlinear ergodic theorems, Nonlinear Analysis 39(2000), 1-10. CMP 2000:03
5.: D. Guo and V. Lakshimikantham, Nonlinear Problems in Abstract Cones, Academic Press, New York, 1988. MR 89k:47084
6.: T. Fujimoto and U. Krause, Asymptotic properties for inhomogeneous iterations of nonlinear operators, SIAM J. Math. Anal. 19(1988), 841-853. MR 90b:47119
7.: T. Fujimoto and U. Krause, Stable inhomogeneous iterations of nonlinear positive operators on Banach spaces, SIAM J. Math. Anal. 25(1994), 1195-1202. MR 95m:47104
8.: H. Inaba, Weak ergodicity of population evolution processes, Math. Biosc. 96(1989), 195-219. MR 91b:92028
9.: J. R. Jachymski, An extension of A. Ostrowski's Theorem on the round-off stability of iterations, Aequ. Math. 53(1997), 242-253. MR 98d:47122
10.: J. P. Keener, The Perron-Frobenius Theorem and the ranking of football teams, SIAM Review 35(1993), 80-93. MR 94a:15012
11.: M. A. Krasnosel'skii and P. P. Zabreiko, Geometrical Methods of Nonlinear Analysis, Springer-Verlag, Berlin, 1984. MR 85b:47057
12.: U. Krause, Path stability of prices in a nonlinear Leontief model, Ann. Oper. Res. 37(1992), 141-148. CMP 93:01
13.: U. Krause, Positive nonlinear systems: some results and applications, Proceedings of the First World Congress of Nonlinear Analysts 1992, W. de Gruyter, Berlin, 1996. CMP 96:12
14.: R. D. Nussbaum, Iterated nonlinear maps and Hilbert's projective metric, Mem. Amer. Math. Soc. Vol.75, No.391 (Sept. 1988). MR 89m:47046
15.: R. D. Nussbaum, Some nonlinear weak ergodic theorems, SIAM. J. Math. Anal. 21(1990), pp. 436-460. MR 90m:47081
16.: E. Seneta, Non-negative Matrices and Markov Chains, 2nd ed., Springer-Verlag, Berlin, 1980; 1st ed., Non-negative Matrice, G. Allen and Unwin, London, 1973. MR 85i:60058
17.: A. C. Thompson, On certain contraction mappings in a partially ordered vector space, Proc. Amer. Math. Soc., 14(1963), 438-443. MR 26:6727

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