Skip to main content
Log in

Asymptotic fixed point theorems for local condensing maps

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Alexandroff, P., Hopf, H.: Topologie. Berlin: Springer 1935.

    Google Scholar 

  2. Borisovic, Ju. G., Sapronov, Ju. I.: A contribution to the topological theory of condensing operators. Soviet. Math. Dokladi9, 1304–1307 (1968).

    Google Scholar 

  3. Browder, F. E.: The topological fixed point theory and its applications to functional analysis. Ph.D. dissertation (Princeton University, 1948).

  4. —— On a generalization of the Schauder fixed point theorem. Duke Math. Jour.26, 291–304 (1959).

    Google Scholar 

  5. —— On the fixed point index for continuous mappings of locally connected spaces. Summa Brasil. Math.4, 253–293 (1960).

    Google Scholar 

  6. —— Another generalization of the Schauder fixed point theorem. Duke Math. Jour.32, 399–406 (1965).

    Google Scholar 

  7. —— A further generalization of the Schauder fixed point theorem. Duke Math. Jour.32, 575–578 (1965).

    Google Scholar 

  8. —— Asymptotic fixed point theorems. Math. Ann.185, 38–61 (1970).

    Google Scholar 

  9. Darbo, G.: Punti uniti in trasformazioni a condominio non compatto. Rend. Sem. Mat. Univ. Padova24, 84–92 (1955).

    Google Scholar 

  10. Deleanu, A.: Theorie des points fixes sur les retractes de voisinage des espaces convexoides. Bull. Soc. Math. France87, 235–243 (1959).

    Google Scholar 

  11. —— Une generalization du theoreme du point fixe de Schauder. Bull. Soc. Math. France89, 223–226 (1961).

    Google Scholar 

  12. Dold, A.: Fixed point index and fixed point theorems for Euclidean neighborhood retracts. Topology4, 1–8 (1965).

    Google Scholar 

  13. Frum-Ketkov, R.L.: On mappings of the sphere of a Banach space. Soviet Math. Dokladi8, 1004–1006 (1967).

    Google Scholar 

  14. Hanner, O.: Some theorems on absolute neighborhood retracts. Arkiv for Matematik1, 389–408 (1951).

    Google Scholar 

  15. Hu, S.: Theory of retracts. Detroit: Wayne State University Press 1965.

    Google Scholar 

  16. Jones, G. S.: The existence of periodic solutions off'(x)=-αf(x-1) [1 +f(x)]. Jour. Math. Anal. Appl.2, 435–450 (1962).

    Google Scholar 

  17. —— Asymptotic fixed point theorems and periodic solutions of functional differential equations. Contrib. Diff. Eqns.2, 385–405 (1963).

    Google Scholar 

  18. —— Periodic motions in Banach space and applications to functional differential equations. Contrib. Diff. Eqns.3, 75–106 (1964).

    Google Scholar 

  19. —— Stability and asymptotic fixed point theory. Proc. Nat. Acad. Sci. U.S.A.53, 1262–1264 (1965).

    Google Scholar 

  20. Kuratowski, C.: Sur les espaces completes. Fund. Math.15, 301–309 (1930).

    Google Scholar 

  21. Lefschetz, S.: Algebraic topology. Amer. Math. Soc. Colloquium Publications, vol. 27, Providence, R.I., 1942.

  22. Leray, J.: Sur la position d'un ensemble ferme de points d'un espace topologique. Jour. de Math. Pures et Appl.24, 169–199 (1945).

    Google Scholar 

  23. —— Sur les equations et les transformations. Jour. de Math. Pures et Appl.24, 201–248 (1945).

    Google Scholar 

  24. —— Theorie des points fixes, indice total et nombre de Lefschetz. Bull. Soc. Math. France87, 221–233 (1959).

    Google Scholar 

  25. Leray, J.: La theorie des points fixes et ses applications en analyse. Proc. Int. Congress Math., Cambridge, vol.2, 202–208 (1950).

    Google Scholar 

  26. Nussbaum, R. D.: The fixed point index and asymptotic fixed point theorems fork-set-contractions. Bull. Amer. Math. Soc.75, 490–495 (1969).

    Google Scholar 

  27. -- The fixed point index for local condensing maps. Ann. Mat. pura appl., (to appear).

  28. -- Degree theory for local condensing maps. J. Math. Anal. and App., (to appear).

  29. -- The fixed point index and fixed point theorems fork-set-contractions. Ph. D. dissertation (University of Chicago, 1969).

  30. O'Neill, B.: Essential sets and fixed points. Amer. Jour. Math.75, 497–509 (1953).

    Google Scholar 

  31. Palais, R. S.: Homotopy theory of infinite dimensional manifolds. Topology5, 1–16 (1966).

    Google Scholar 

  32. Petryshyn, W. V.: On the approximation-solvability of nonlinear equations. Math. Ann.177, 156–164 (1968).

    Google Scholar 

  33. Sadovskii, B. N.: On a fixed point principle. Functional Analysis and Appl.1, 74–76 (1967).

    Google Scholar 

  34. Thompson, R. B.: A unified approach to local and global fixed point indices. Advances in Math.3, 1–72 (1969).

    Google Scholar 

  35. Yoshizawa, T.: Stable sets and periodic solutions in a perturbed system. Contrib. Diff. Eqns.2, 407–420 (1963).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nussbaum, R.D. Asymptotic fixed point theorems for local condensing maps. Math. Ann. 191, 181–195 (1971). https://doi.org/10.1007/BF01578707

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01578707

Keywords

Navigation