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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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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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