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A generalization of the Schauder fixed point theorem via multivalued contractions. (English) Zbl 1068.47070
Summary: We establish a fixed point theorem for a continuous function $$f:X\to E$$, where $$E$$ is a Banach space and $$X\subseteq E$$. Our result, which involves multivalued contractions, contains the classical Schauder fixed point theorem as a special case. An application is presented.
##### MSC:
 47H10 Fixed-point theorems 47H04 Set-valued operators
##### Keywords:
fixed points; multivalued contractions; absolute retracts
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