The existence of nonexpansive retractions in Banach spaces

Norimichi HIRANO; Kazuo KIDO; Wataru TAKAHASHI

doi:10.2969/jmsj/03810001

Norimichi HIRANO, Kazuo KIDO, Wataru TAKAHASHI

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ジャーナルフリー

1986 年 38 巻 1 号 p. 1-7

DOI https://doi.org/10.2969/jmsj/03810001

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Published: 1986 Received: 1984/05/28 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) J. B. Baillon, Un théorème de type ergodique pour les contractions non linéaires daps un espace de Hilbert, C. R. Acad. Sci. Paris, 280 (1975), 1511-1514.
2) F. E. Browder, “Nonlinear operators and nonlinear equations of evolutions in Banach spaces”. Proc. Symposia in Pure Math., 18-2, Amer. Math. Soc., 1976.
3) R. E. Bruck, A simple proof of the mean ergodic theorem for nonlinear contractions in Banach spaces, Israel J. Math., 32 (1979), 107-116.
4) 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.
5) K. Goebel and S. Reich, “Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings”. Pure and Applied Mathematics, 83 (1984), Marcel Dekker.
6) N. Hirano, A proof of the mean ergodic theorem for nonexpansive mappings in Banach space, Proc. Amer. Math. Soc., 78 (1980), 361-365.
7) N. Hirano and W. Takahashi, Nonlinear ergodic theorems for an amenable semigroup of nonexpansive mappings in a Banach space, Pacific J. Math., 112 (1984), 333-346.
8) K. Kido and W. Takahashi, Mean ergodic theorems for semigroups of linear continuous operators in Banach spaces, J. Math. Anal. Appl., 103 (1984), 387-394.
9) K. Kido and W. Takahashi, Means on commutative semigroups and nonlinear ergodic theorems, to appear in J. Math. Anal. Appl.
10) S. Reich, Weak convergence theorems for nonexpansive mappings in Banach spaces, J. Math. Anal. Appl., 67 (1979), 274-276.
11) G. Rodé, An ergodic theorem for semigroups of nonexpansive mappings in a Hilbert space, J. Math. Anal. Appl., 85 (1982), 172-178.
12) W. Takahashi, Invariant functions for amenable semigroups of positive contractions on L¹, Kodai Math. Sem. Rep., 23 (1971), 131-143.
13) W. Takahashi, A nonlinear ergodic theorem for an amenable semigroup of nonexpansive mappings in a Hilbert space, Proc. Amer. Math. Soc., 81 (1981), 253-256.

Right : [1] J. B. Baillon, Un théorème de type ergodique pour les contractions non linéaires daps un espace de Hilbert, C. R. Acad. Sci. Paris, 280 (1975), 1511-1514.
[2] F. E. Browder, “Nonlinear operators and nonlinear equations of evolutions in Banach spaces”. Proc. Symposia in Pure Math., 18-2, Amer. Math. Soc., 1976.
[3] R. E. Bruck, A simple proof of the mean ergodic theorem for nonlinear contractions in Banach spaces, Israel J. Math., 32 (1979), 107-116.
[4] 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.
[5] K. Goebel and S. Reich, “Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings”, Pure and Applied Mathematics, 83 (1984), Marcel Dekker.
[6] N. Hirano, A proof of the mean ergodic theorem for nonexpansive mappings in Banach space, Proc. Amer. Math. Soc., 78 (1980), 361-365.
[7] N. Hirano and W. Takahashi, Nonlinear ergodic theorems for an amenable semigroup of nonexpansive mappings in a Banach space, Pacific J. Math., 112 (1984), 333-346.
[8] K. Kido and W. Takahashi, Mean ergodic theorems for semigroups of linear continuous operators in Banach spaces, J. Math. Anal. Appl., 103 (1984), 387-394.
[9] K. Kido and W. Takahashi, Means on commutative semigroups and nonlinear ergodic theorems, to appear in J. Math. Anal. Appl.
[10] S. Reich, Weak convergence theorems for nonexpansive mappings in Banach spaces, J. Math. Anal. Appl., 67 (1979), 274-276.
[11] G. Rodé, An ergodic theorem for semigroups of nonexpansive mappings in a Hilbert space, J. Math. Anal. Appl., 85 (1982), 172-178.
[12] W. Takahashi, Invariant functions for amenable semigroups of positive contractions on L¹, Kodai Math. Sem. Rep., 23 (1971), 131-143.
[13] W. Takahashi, A nonlinear ergodic theorem for an amenable semigroup of nonexpansive mappings in a Hilbert space, Proc. Amer. Math. Soc., 81 (1981), 253-256.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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