On the Schauder fixed point theorem

Lech Górniewicz; Danuta Rozpłoch-Nowakowska

Banach Center Publications (1996)

  • Volume: 35, Issue: 1, page 207-219
  • ISSN: 0137-6934

Abstract

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The paper contains a survey of various results concerning the Schauder Fixed Point Theorem for metric spaces both in single-valued and multi-valued cases. A number of open problems is formulated.

How to cite

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Górniewicz, Lech, and Rozpłoch-Nowakowska, Danuta. "On the Schauder fixed point theorem." Banach Center Publications 35.1 (1996): 207-219. <http://eudml.org/doc/251331>.

@article{Górniewicz1996,
abstract = {The paper contains a survey of various results concerning the Schauder Fixed Point Theorem for metric spaces both in single-valued and multi-valued cases. A number of open problems is formulated.},
author = {Górniewicz, Lech, Rozpłoch-Nowakowska, Danuta},
journal = {Banach Center Publications},
keywords = {absolute retract; set-valued operators; degree; fixed point; multivalued map; Schauder fixed point theorem; compact map; Banach space; metric spaces},
language = {eng},
number = {1},
pages = {207-219},
title = {On the Schauder fixed point theorem},
url = {http://eudml.org/doc/251331},
volume = {35},
year = {1996},
}

TY - JOUR
AU - Górniewicz, Lech
AU - Rozpłoch-Nowakowska, Danuta
TI - On the Schauder fixed point theorem
JO - Banach Center Publications
PY - 1996
VL - 35
IS - 1
SP - 207
EP - 219
AB - The paper contains a survey of various results concerning the Schauder Fixed Point Theorem for metric spaces both in single-valued and multi-valued cases. A number of open problems is formulated.
LA - eng
KW - absolute retract; set-valued operators; degree; fixed point; multivalued map; Schauder fixed point theorem; compact map; Banach space; metric spaces
UR - http://eudml.org/doc/251331
ER -

References

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  1. [B] K. Borsuk, Theory of Retracts, Monografie Matematyczne PAN, PWN Warszawa 1967. Zbl0153.52905
  2. [CB] C. Bowszyc, Some theorems in the Theory of Fixed Points, (Thesis), University of Warsaw (1969), (in Polish). 
  3. [FB] F. E. Browder, The fixed point theory of multi-valued mappings in topological vector spaces, Math. Ann. 177 (1968), 283-301. Zbl0176.45204
  4. [D] K. Deimling, Nonlinear Functional Analysis, Springer-Verlag Berlin Heidelberg New York Tokyo 1985. Zbl0559.47040
  5. [DG] J. Dugundji and A. Granas, Fixed Point Theory, Vol. 1, Monografie Matematyczne PAN, PWN Warszawa 1982. Zbl0483.47038
  6. [FG] G. Fournier and L. Górniewicz, The Lefschetz fixed point theorem for some non-compact multi-valued maps, Fundamenta Mathematicae XCIV (1977). Zbl0342.55007
  7. [F1] G. Fournier, Théorème de Lefschetz, I - Applications éventuellement compactes, Bull. Acad. Polon. Sci. 6 (1975), 693-701. Zbl0307.55006
  8. [F2] G. Fournier, Théorème de Lefschetz, II - Applications d'attraction compacte, ibid., 701-706. Zbl0307.55007
  9. [F3] G. Fournier, Théorème de Lefschetz, III - Applications asymptotiquement compactes, ibid., 707-713. 
  10. [LG] L. Górniewicz, Homological methods in fixed point theory of multivalued maps, Dissertationes Math. 129 (1976), Warszawa. 
  11. [AG] A. Granas, Points Fixes pour les Applications Compactes: Espaces de Lefschetz et la Theorie de l'Indice, SMS, Montreal 68 (1980). Zbl0456.55001
  12. [AG1] A. Granas, Generalizing the Hopf-Lefschetz fixed point theorem for non-compact ANR-s, Symposium on Infinite Dimensional Topology, Bâton-Rouge, 1967. 
  13. [S] J. Schauder, Der Fixpunktsatz in Funktionalräumen, Studia Math. 2 (1930), 171-180. Zbl56.0355.01
  14. [W] A. Wieczorek, Survey of Results on Kakutani Property of Spaces with generalized Convexity, Fixed Point Theory and its Applications, Pitman Research Notes in Mathematics Series No. 252 (1990), 453-461. Zbl0757.54032

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