Opial's property and James' quasi-reflexive spaces
Tadeusz Kuczumow; Simeon Reich
Commentationes Mathematicae Universitatis Carolinae (1994)
- Volume: 35, Issue: 2, page 283-289
- ISSN: 0010-2628
Access Full Article
topAbstract
topHow to cite
topReferences
top- Aksoy A.G., Khamsi M.A., Nonstandard Methods in Fixed Point Theory, Springer-Verlag, New York, 1990. Zbl0713.47050MR1066202
- Andrew A., Spreading basic sequences and subspaces of James' quasi-reflexive space, Math. Scan. 48 (1981), 109-118. (1981) Zbl0439.46010MR0621422
- Brodskii M.S., Milman D.P., On the center of a convex set, Dokl. Akad. Nauk SSSR 59 (1948), 837-840. (1948) MR0024073
- Goebel K., Kirk W.A., Topics in Metric Fixed Point Theory, Cambridge University Press, Cambridge, 1990. MR1074005
- Goebel K., Reich S., Uniform Convexity, Hyperbolic Geometry and Nonexpansive Mappings, Marcel Dekker, New York and Basel, 1984. Zbl0537.46001MR0744194
- Goebel K., Sekowski T., Stachura A., Uniform convexity of the hyperbolic metric and fixed points of holomorphic mappings in the Hilbert ball, Nonlinear Analysis 4 (1980), 1011-1021. (1980) Zbl0448.47048MR0586863
- Gǫrnicki J., Some remarks on almost convergence of the Picard iterates for nonexpansive mappings in Banach spaces which satisfy the Opial condition, Comment. Math. 29 (1988), 59-68. (1988) MR0988960
- Gossez J.P., Lami Dozo E., Some geometric properties related to the fixed point theory for nonexpansive mappings, Pacific J. Math. 40 (1972), 565-573. (1972) MR0310717
- James R.C., Bases and reflexivity of Banach spaces, Ann. of Math. 52 (1950), 518-527. (1950) Zbl0039.12202MR0039915
- James R.C., A non-reflexive Banach space isometric with its second conjugate space, Proc. Nat. Acad. Sci. USA 37 (1951), 134-137. (1951) MR0044024
- James R.C., A separable somewhat reflexive Banach space with nonseparable dual, Bull. Amer. Math. Soc. 80 (1974), 738-743. (1974) Zbl0286.46018MR0417763
- James R.C., Banach spaces quasi-reflexive of order one, Studia Math. 60 (1977), 157-177. (1977) Zbl0356.46017MR0461099
- Karlovitz L.A., On nonexpansive mappings, Proc. Amer. Math. Soc. 55 (1976), 321-325. (1976) Zbl0328.47033MR0405182
- Khamsi M.A., James' quasi-reflexive space has the fixed point property, Bull. Austral. Math. Soc. 39 (1989), 25-30. (1989) Zbl0672.47045MR0976257
- Khamsi M.A., Normal structure for Banach spaces with Schauder decomposition, Canad. Math. Bull. 32 (1989), 344-351. (1989) Zbl0647.46016MR1010075
- Khamsi M.A., On uniform Opial condition and uniform Kadec-Klee property in Banach and metric spaces, preprint. Zbl0854.47035MR1380728
- Kirk W.A., A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly 72 (1965), 1004-1006. (1965) Zbl0141.32402MR0189009
- Kuczumow T., Weak convergence theorems for nonexpansive mappings and semigroups in Banach spaces with Opial's property, Proc. Amer. Math. Soc. 93 (1985), 430-432. (1985) Zbl0585.47043MR0773996
- Lindenstrauss J., Stegall C., Examples of separable spaces which do not contain and whose duals are non-separable, Studia Math. 54 (1975), 81-105. (1975) MR0390720
- Lindenstrauss J., Tzafriri L., Classical Banach Spaces, Vol. I and II, Springer-Verlag, BerlinHeidelberg-New York, 1977 and 1979. MR0415253
- Opial Z., Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967), 591-597. (1967) Zbl0179.19902MR0211301
- Opial Z., Nonexpansive and Monotone Mappings in Banach Spaces, Lecture Notes 61-1, Center for Dynamical Systems, Brown University, Providence, R.I., 1967.
- Prus S., Banach spaces with the uniform Opial property, Nonlinear Analysis 18 (1992), 697-704. (1992) Zbl0786.46023MR1160113
- Tingley D., The normal structure of James' quasi-reflexive space, Bull. Austral. Math. Soc. 42 (1990), 95-100. (1990) Zbl0724.46014MR1066363