Fixed point theorems for nonexpansive maps in Banach spaces |
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Authors: | Smaïl Djebali Karima Hammache |
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Institution: | Department of Mathematics, E.N.S., P.B. 92, 16050 Kouba, Algiers, Algeria |
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Abstract: | In this work, we present some new versions of fixed point theorems for nonexpansive maps and 1-set contractions defined on closed, convex, not necessarily bounded subsets of Banach spaces. Our proofs rely on a compactness result for an approximate fixed point set. The Kuratowski measure of noncompactness is used throughout. To illustrate the results obtained, some applications to Banach algebras and Hammerstein integral equations are provided. |
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Keywords: | primary 47H09 secondary 47B48 47H10 47J25 47N20 |
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