On the approximate fixed point property in abstract spaces

Mathematische Zeitschrift

Volumn 271, Issue 3-4, 2012, Pages 1271-1285

  Barroso, C S ^a   Kalenda, O F K ^b   Lin, P K ^c  

^a FEDERAL UNIVERSITY OF CEARÁ   (Brazil)

^b CHARLES UNIVERSITY   (Czech Republic)

^c University of Memphis   (United States)

Author keywords

1 sequence; Fr chet Urysohn space; Metrizable locally convex space; Weak approximate fixed point property

Indexed keywords

EID: 84864383537     PISSN: 00255874     EISSN: 14321823     Source Type: Journal    
DOI: 10.1007/s00209-011-0915-6     Document Type: Article

References (27)

1. Archangel'skii, A. V.: Topological Spaces of Functions, Moscow State Univ. (1989) (in Russian). Kluwer Academic Publication, Dordrecht, Boston, London (1992) (in English).
2. Asplund E.: Fréchet differentiability of convex functions. Acta Math. 121, 31-47 (1968).
3. Barroso C. S.: The approximate fixed point property in Hausdorff topological vector spaces and applications. Discrete Cont. Dyn. Syst. 25, 467-479 (2009).
4. Barroso C. S., Lin P.-K.: On the weak approximate fixed point property. J. Math. Anal. Appl. 365, 171-175 (2010).
5. Domínguez Benavides T., Japon Pineda M. A., Prus S.: Weak compactness and fixed point property for affine mappings. J. Funct. Anal. 209(1), 1-15 (2004).
6. Domínguez Benavides T.: A renorming of some nonseparable Banach spaces with the fixed point property. J. Math. Anal. Appl. 350, 525-530 (2009).
7. Bourgain J., Fremlin D. H., Talagrand M.: Pointwise compact sets of Baire measurable functions. Am. J. Math. 100, 845-886 (1978).
8. Brânzei R., Morgan J., Scalzo V.: Approximate fixed point theorems in Banach spaces with applications in game theory. J. Math. Anal. Appl. 285, 619-628 (2003).
9. p(μ)-spaces. Can. Math. Bull. 32, 169-176 (1989).
10. Fabian M.: Gâteaux differentiability of convex functions and topology: weak Asplund spaces. Wiley-Interscience, New York (1997).
11. Fan K.: Sur un théorème minimax. C. R. Acad. Sci. Paris 259, 3925-3928 (1964).
12. Hazewinkel M., van de Vel M.: On almost-fixed point theory. Can. J. Math. 30, 673-699 (1978).
13. Idzik A.: On γ-almost fixed point theorems. The single-valued case. Bull. Polish. Acad. Sci. Math. 35, 461-464 (1987).
14. Idzik A.: Almost fixed point theorems. Proc. Am. Math. Soc. 104, 779-784 (1988).
15. Jafari F., Sehgal V. M.: Some fixed point theorems for nonconvex spaces. Int. J. Math. & Math. Sci. 21, 133-138 (1998).
16. Johnson W. B., Lindenstrauss J.: Some remarks on weakly compactly generated Banach spaces. Israel J. Math. 17, 219-230 (1974).
17. Kalenda O. F. K.: Valdivia compact spaces in topology and Banach space theory. Extracta Math. 15(1), 1-85 (2000).
18. 1 have weak approximate fixed point property. J. Math. Anal. Appl. 373, 134-137 (2011).
19. Köthe G.: Topological Vector Spaces I. Springer-Verlag, New York (1969).
20. Lin P.-K., Sternfeld Y.: Convex sets with the Lipschitz fixed point property are compact. Proc. Am. Math. Soc. 93, 633-639 (1985).
21. Moloney J., Weng X.: A fixed point theorem for demicontinuous pseudocontractions in Hilbert spaces. Studia Math. 116(3), 217-223 (1995).
22. Namioka I., Phelps R. R.: Banach spacess which are Asplund spaces. Duke Math. J. 42(4), 735-750 (1975).
23. 1. Proc. Nat. Acad. Sci. USA 71(6), 2411-2413 (1974).
24. Tijs S. H., Torre A., Branzei R.: Approximate fixed point theorems. Libertas Math. 23, 35-39 (2003).
25. Troyanski S. L.: On locally uniformly convex and differentiable norms in certain non-separable Banach spaces. Studia Math. 37, 173-180 (1971).
26. van de Vel, M., The intersection property: a contribution to almost fixed point theory, Thesis, University of Imtelling Antewerpen, 1975.
27. van der Walt, T.: Fixed and almost fixed points, Thesis, Math. Centre, Amsterdam, 1963.