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ArticleOriginal scientific text

Title

On the Schauder fixed point theorem

Authors 1, 1

Affiliations

  1. Department of Mathematics and Informatics, Nicholas Copernicus University, ul. Chopina 12/18, Toruń, Poland

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.

Keywords

ENG
absolute retract, set-valued operators, degree, fixed point

Bibliography

  1. [B] K. Borsuk, Theory of Retracts, Monografie Matematyczne PAN, PWN Warszawa 1967.
  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.
  4. [D] K. Deimling, Nonlinear Functional Analysis, Springer-Verlag Berlin Heidelberg New York Tokyo 1985.
  5. [DG] J. Dugundji and A. Granas, Fixed Point Theory, Vol. 1, Monografie Matematyczne PAN, PWN Warszawa 1982.
  6. [FG] G. Fournier and L. Górniewicz, The Lefschetz fixed point theorem for some non-compact multi-valued maps, Fundamenta Mathematicae XCIV (1977).
  7. [F1] G. Fournier, Théorème de Lefschetz, I - Applications éventuellement compactes, Bull. Acad. Polon. Sci. 6 (1975), 693-701.
  8. [F2] G. Fournier, Théorème de Lefschetz, II - Applications d'attraction compacte, ibid., 701-706.
  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).
  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.
  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.
Banach Center Publications
1996/35/1
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Pages:
207-219
Main language of publication
English
Published
1996
Exact and natural sciences