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Leray-Schauder principles for condensing multivalued mappings in topological linear spaces


Author: Rainald Schöneberg
Journal: Proc. Amer. Math. Soc. 72 (1978), 268-270
MSC: Primary 47H10
DOI: https://doi.org/10.1090/S0002-9939-1978-0507320-9
MathSciNet review: 507320
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Abstract: By establishing the existence of an equivalent fixed point problem it is shown without any recourse to degree theory or to the theory of homotopy-extension-theorems that all fixed point theorems of Leray-Schauder type for condensing (single- or multi-valued) mappings in topological linear spaces can immediately be deduced from the corresponding fixed point theorems of Schauder type.


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  • [1] F. E. Browder, Problèmes non-linéaires, Les presses de l'Univ. de Montréal, Montréal, Que., 1966. MR 40 #3380. MR 0250140 (40:3380)
  • [2] D. E. Edmunds and J. R. L. Webb, A Leray-Schauder theorem, Math. Ann. 182 (1969), 207-212. MR 0254688 (40:7895)
  • [3] P. M. Fitzpatrick and W. V. Petryshyn, Fixed point theorems for multivalued noncompact acyclic mappings, Pacific J. Math. 54 (1974), 17-23. MR 0405179 (53:8973)
  • [4] -, Fixed point theorems and the fixed point index for multivalued mappings in cones, J. London Math. Soc. 12 (1975), 75-85. MR 0405180 (53:8974)
  • [5] A. Granas, Colloquium talk, Aachen, 1975 (unpublished).
  • [6] S. Hahn, A remark on a fixed point theorem for condensing set-valued mappings, Technische Universität Dresden, Informationen, July 1977.
  • [7] W. V. Petryshyn, Structure of the fixed point set of k-set-contractions, Arch. Rational Mech. Anal. 40 (1971), 312-328. MR 0273480 (42:8358)
  • [8] W. V. Petryshyn and P. M. Fitzpatrick, A degree theory, fixed point theorems and mapping theorems for multivalued noncompact mappings, Trans. Amer. Math. Soc. 194 (1974), 1-25. MR 2478129 (2010c:47213)
  • [9] A. J. B. Potter, An elementary version of the Leray-Schauder theorem, J. London Math. Soc. 5 (1972), 414-416. MR 0312342 (47:904)
  • [10] J. R. L. Webb, A fixed point theorem and applications to functional equations in Banach spaces, Boll. Un. Mat. Ital. 4 (1971), 775-788. MR 0377631 (51:13802)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0507320-9
Keywords: Measure of noncompactness, condensing, fixed point theorem of Leray-Schauder type
Article copyright: © Copyright 1978 American Mathematical Society

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