| Title:
|
Opial's property and James' quasi-reflexive spaces (English) |
| Author:
|
Kuczumow, Tadeusz |
| Author:
|
Reich, Simeon |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
35 |
| Issue:
|
2 |
| Year:
|
1994 |
| Pages:
|
283-289 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Two of James' three quasi-reflexive spaces, as well as the James Tree, have the uniform $w^{\ast }$-Opial property. (English) |
| Keyword:
|
fixed points |
| Keyword:
|
James' quasi-reflexive spaces |
| Keyword:
|
James Tree |
| Keyword:
|
nonexpansive mappings |
| Keyword:
|
Opial's property |
| Keyword:
|
the demiclosedness principle |
| MSC:
|
46B10 |
| MSC:
|
46B20 |
| MSC:
|
46B25 |
| MSC:
|
47H10 |
| idZBL:
|
Zbl 0818.46019 |
| idMR:
|
MR1286575 |
| . |
| Date available:
|
2009-01-08T18:11:00Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118667 |
| . |
| Reference:
|
[1] Aksoy A.G., Khamsi M.A.: Nonstandard Methods in Fixed Point Theory.Springer-Verlag, New York, 1990. Zbl 0713.47050, MR 1066202 |
| Reference:
|
[2] Andrew A.: Spreading basic sequences and subspaces of James' quasi-reflexive space.Math. Scan. 48 (1981), 109-118. Zbl 0439.46010, MR 0621422 |
| Reference:
|
[3] Brodskii M.S., Milman D.P.: On the center of a convex set.Dokl. Akad. Nauk SSSR 59 (1948), 837-840. MR 0024073 |
| Reference:
|
[4] Goebel K., Kirk W.A.: Topics in Metric Fixed Point Theory.Cambridge University Press, Cambridge, 1990. MR 1074005 |
| Reference:
|
[5] Goebel K., Reich S.: Uniform Convexity, Hyperbolic Geometry and Nonexpansive Mappings.Marcel Dekker, New York and Basel, 1984. Zbl 0537.46001, MR 0744194 |
| Reference:
|
[6] 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. Zbl 0448.47048, MR 0586863 |
| Reference:
|
[7] 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. MR 0988960 |
| Reference:
|
[8] 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. MR 0310717 |
| Reference:
|
[9] James R.C.: Bases and reflexivity of Banach spaces.Ann. of Math. 52 (1950), 518-527. Zbl 0039.12202, MR 0039915 |
| Reference:
|
[10] James R.C.: A non-reflexive Banach space isometric with its second conjugate space.Proc. Nat. Acad. Sci. USA 37 (1951), 134-137. MR 0044024 |
| Reference:
|
[11] James R.C.: A separable somewhat reflexive Banach space with nonseparable dual.Bull. Amer. Math. Soc. 80 (1974), 738-743. Zbl 0286.46018, MR 0417763 |
| Reference:
|
[12] James R.C.: Banach spaces quasi-reflexive of order one.Studia Math. 60 (1977), 157-177. Zbl 0356.46017, MR 0461099 |
| Reference:
|
[13] Karlovitz L.A.: On nonexpansive mappings.Proc. Amer. Math. Soc. 55 (1976), 321-325. Zbl 0328.47033, MR 0405182 |
| Reference:
|
[14] Khamsi M.A.: James' quasi-reflexive space has the fixed point property.Bull. Austral. Math. Soc. 39 (1989), 25-30. Zbl 0672.47045, MR 0976257 |
| Reference:
|
[15] Khamsi M.A.: Normal structure for Banach spaces with Schauder decomposition.Canad. Math. Bull. 32 (1989), 344-351. Zbl 0647.46016, MR 1010075 |
| Reference:
|
[16] Khamsi M.A.: On uniform Opial condition and uniform Kadec-Klee property in Banach and metric spaces.preprint. Zbl 0854.47035, MR 1380728 |
| Reference:
|
[17] Kirk W.A.: A fixed point theorem for mappings which do not increase distances.Amer. Math. Monthly 72 (1965), 1004-1006. Zbl 0141.32402, MR 0189009 |
| Reference:
|
[18] 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. Zbl 0585.47043, MR 0773996 |
| Reference:
|
[19] Lindenstrauss J., Stegall C.: Examples of separable spaces which do not contain $l_1$ and whose duals are non-separable.Studia Math. 54 (1975), 81-105. MR 0390720 |
| Reference:
|
[20] Lindenstrauss J., Tzafriri L.: Classical Banach Spaces, Vol. I and II.Springer-Verlag, BerlinHeidelberg-New York, 1977 and 1979. MR 0415253 |
| Reference:
|
[21] Opial Z.: Weak convergence of the sequence of successive approximations for nonexpansive mappings.Bull. Amer. Math. Soc. 73 (1967), 591-597. Zbl 0179.19902, MR 0211301 |
| Reference:
|
[22] Opial Z.: Nonexpansive and Monotone Mappings in Banach Spaces.Lecture Notes 61-1, Center for Dynamical Systems, Brown University, Providence, R.I., 1967. |
| Reference:
|
[23] Prus S.: Banach spaces with the uniform Opial property.Nonlinear Analysis 18 (1992), 697-704. Zbl 0786.46023, MR 1160113 |
| Reference:
|
[24] Tingley D.: The normal structure of James' quasi-reflexive space.Bull. Austral. Math. Soc. 42 (1990), 95-100. Zbl 0724.46014, MR 1066363 |
| . |
