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1995 | 68 | 1 | 17-23
Tytuł artykułu

Weak uniform normal structure and iterative fixed points of nonexpansive mappings

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EN
Abstrakty
EN
This paper is concerned with weak uniform normal structure and iterative fixed points of nonexpansive mappings. Precisely, in Section 1, we show that the geometrical coefficient β(X) for a Banach space X recently introduced by Jimenez-Melado [8] is exactly the weakly convergent sequence coefficient WCS(X) introduced by Bynum [1] in 1980. We then show in Section 2 that all kinds of James' quasi-reflexive spaces have weak uniform normal structure. Finally, in Section 3, we show that in a space X with weak uniform normal structure, every nonexpansive self-mapping defined on a weakly sequentially compact convex subset of X admits an iterative fixed point.
Rocznik
Tom
68
Numer
1
Strony
17-23
Opis fizyczny
Daty
wydano
1995
otrzymano
1994-01-03
Twórcy
  • Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Apdo. 1160, 41080 Sevilla, Spain
  • Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Apdo. 1160, 41080 Sevilla, Spain
autor
  • Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Apdo. 1160, 41080 Sevilla, Spain
Bibliografia
  • [1] W. L. Bynum, Normal structure coefficients for Banach spaces, Pacific J. Math. 86 (1980), 427-436.
  • [2] T. Domínguez Benavides, Weak uniform normal structure in direct-sum spaces, Studia Math. 103 (1992), 283-290.
  • [3] T. Domínguez Benavides, Some properties of the set and ball measures of noncompactness and applications, J. London Math. Soc. 34 (1986), 120-128.
  • [4] T. Domínguez Benavides and G. López Acedo, Lower bounds for normal structure coefficients, Proc. Roy. Soc. Edinburgh 121A (1992), 245-252.
  • [5] M. Edelstein and R. C. O'Brien, Nonexpansive mappings, asymptotic regularity, and successive approximations, J. London Math. Soc. 17 (1978), 547-554.
  • [6] K. Goebel and W. A. Kirk, Topics in Metric Fixed Point Theory, Cambridge University Press, 1990.
  • [7] S. Ishikawa, Fixed points and iteration of a nonexpansive mapping in a Banach space, Proc. Amer. Math. Soc. 59 (1976), 65-71.
  • [8] A. Jimenez-Melado, Stability of weak normal structure in James quasi reflexive space, Bull. Austral. Math. Soc. 46 (1992), 367-372.
  • [9] M. A. Khamsi, James quasi reflexive space has the fixed point property, ibid. 39 (1989), 25-30.
  • [10] W. A. Kirk, A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly 72 (1965), 1004-1006.
  • [11] E. Maluta, Uniformly normal structure and related coefficients for Banach spaces, Pacific J. Math. 111 (1984), 357-369.
  • [12] P. M. Soardi, Schauder bases and fixed points of nonexpansive mappings, Pacific J. Math. 101 (1982), 193-198.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-cmv68i1p17bwm
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