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Abstrakty
In this paper, we prove that a banach space X with the property (L) with respect to the function [ro](r,s) has the uniform Opial property if and only if [ro](1,s)>1 for any s>0. The criterion in order that an Orlicz sequence space equipped with the Luxemburg norm has the property (L) is given.
Słowa kluczowe
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Rocznik
Tom
Strony
301--309
Opis fizyczny
Bibliogr. 15 poz.
Twórcy
autor
- Department of Mathematics, Harbin University of Science and Technology, Harbin, 150080, P.R. China
autor
- Department of Mathematics, Harbin University of Science and Technology, Harbin, 150080, P.R. China
Bibliografia
- [1] S. T. Chen, Geometry of Orlicz Spaces, Dissertationes Mathematicae, 356, Warszawa, 1996.
- [2] S. T. Chen, H. Hudzik and H. Y. Sun, Complemented copies of l1 in Orlicz spaces, Math. Nachr. 158 (1997), 299-309.
- [3] J. Diestel, Sequence and Series in Banach Spaces, Graduate Texts in Mathematics, Springer-Verlag, 1984.
- [4] P. R. Dowling, C. J. Lennard and B. Turett, Reflexivity and the fixed-point property for nonexpansive maps, J. Math. Anal. Appl. 200 (1996), 653-662.
- [5] J. García-Falset, Stability and fixed points for nonexpansive mappings, Houston Math. 20 (1994), 495-505.
- [6] H. Goebel and W. A. Kirk, Topics in Metric Fixed Point Theory, Cambridge University Press, 1990.
- [7] M. A. Khamsi, An uniform Opial condition and uniform Kadec-Klee property in Banach and metric spaces, Nonlinear Anal. Th. Meth. Appl. 26 (1996), 1733-1748.
- [8] T. C. Lim, Asymptotic centers and nonexpansive mappings in some conjugate spaces, Pac. J. Math. 90, (1980) 135-143.
- [9] Pei-Kee Lin, Kok-Keong Tan and Hong-Kun Xu, Semiemiclosedness principle and asymptotic behavior for asymptotically nonexpansive mappings, Nonlinear Anal. Th. Meth. Appl. 24 (1995), 929-946.
- [10] J. Musielak, Orlicz Spaces and Modular Spaces, Lecture Notes in Math. 1034, 1983.
- [11] Z. Opial, Weak convergence of the sequence of successive approximations for non expansive mappings, Bull. Amer. Math. Soc. 73 (1967), 591-597.
- [12] S. Prus, Banach spaces with uniform Opial property, Nonlinear Anal. Th. Meth. Appl. 8 (1992), 697-704.
- [13] M. M. Rao and Z. D. Ren, Theory of Orlicz Spaces, Marcel Dekker Inc., New York-Basel-Hong Kong, 1991.
- [14] B. Sims and M. Smith, On non-uniform conditions given weak normal structure, Questiones Math. 18 (1995), 9-19.
- [15] K. Tan and H. Xu, On fixed point theorems of nonexpansive mappings in product spaces, Proc. Amer. Math. Soc. 113 (1991), 983-989.
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Bibliografia
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bwmeta1.element.baztech-article-BUS2-0002-0080