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FIXED POINTS OF COUNTABLY CONDENSING MAPPINGS AND ITS APPLICATION TO NONLINEAR EIGENVALUE PROBLEMS

  • KIM IN-SOOK (Department of Mathematics Sungkyunkwan University)
  • Published : 2006.01.01

Abstract

Based on the Schauder fixed point theorem, we give a Leray-Schauder type fixed point theorem for countably condensing mappings in a more general setting and apply it to obtain eigenvalue results on condensing mappings in a simple proof. Moreover, we present a generalization of Sadovskii's fixed point theorem for count ably condensing self-mappings due to S. J. Daher.

Keywords

References

  1. R. R. Akhmerov, M. I. Kamenskii, A. S. Potapov, A. E. Rodkina, and B. N. Sadovskii, Measures of Noncompactness and Condensing Operators, Birkhauser, Basel, 1992
  2. J. M. Ayerbe Toledano, T. Dominguez Benavides, and G. Lopez Acedo, Mea- sures of Noncompactness in Metric Fixed Point Theory, Birkhauser, Basel, 1997
  3. S. J. Daher, On a a fixed point principle of Sadovskii, Nonlinear Anal. 2 (1978), 643-645 https://doi.org/10.1016/0362-546X(78)90012-3
  4. G. Darbo, Punti uniti in trasformazioni a codominio non compatto (Italian), Rend. Sem. Mat. Univ. Padova 24 (1955), 84-92
  5. J. Dugundji, An extension of Tietze's theorem, Pacific J. Math. 1 (1951), 353- 367
  6. S. Hahn, Eigenwertaussagen fur kompakte und kondensierende mengenwertige Abbildungen in topologischen Vektorraumen, Comment. Math. Univ. Carolin. 20 (1979), 123-141
  7. S. Hahn, Ein Homotopieerweiterungssatz fur konzentrierende mengenwertige Abbildungen in lokalkonvexen topologischen Vektorraumen, Studia Math. 66 (1979), 107-117 https://doi.org/10.4064/sm-66-2-107-117
  8. C. J. Himmelberg, Fixed points of compact multifunctions, J. Math. Anal. Appl. 38 (1972), 205-207 https://doi.org/10.1016/0022-247X(72)90128-X
  9. H. Monch, Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces, Nonlinear Anal. 4 (1980), 985-999 https://doi.org/10.1016/0362-546X(80)90010-3
  10. E. H. Rothe, Zur Theorie der topologischen Ordunung und der Vektorfelder in Banachschen Raumen, Comp. Math. 5 (1938), 177-197
  11. B. N. Sadovskii, On a fixed point principle (Russian), Funkcional. Anal. i Prilo-zen. 1 (1967), no. 2, 74-76
  12. J. Schauder, Der Fixpunktsatz in Funktionalraumen, Studia Math. 2 (1930), 171-180 https://doi.org/10.4064/sm-2-1-171-180
  13. M. Vath, Fixed point theorems and fixed point index for countably condensing maps, Topol. Methods Nonlinear Anal. 13 (1999), 341-363 https://doi.org/10.12775/TMNA.1999.018

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