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Two results in metric fixed point theory. (English) Zbl 1137.47042
The authors establish two fixed point theorems for certain mappings of contractive type. The first result is concerned with the case where such mappings take a nonempty, closed subset of a complete metric space \(X\) into \(X\), and the second with an application of the continuation method to the case where they satisfy the Leray–Schauder boundary condition in Banach spaces.

MSC:
47H10 Fixed-point theorems
54H25 Fixed-point and coincidence theorems (topological aspects)
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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