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Fixed point theory for self maps between Fréchet spaces. (English) Zbl 0997.47044

The compression-expansion Krasnoselskij’s fixed point theorem in a cone of a Banach space is extended to Fréchet spaces. An application to the existence of nontrivial continuous solutions of a nonlinear integral equation on the half-line is presented to illustrate the theory. An analogous result for multivalued upper semicontinuous \(k\)-set contractive mappings is also obtained.

MSC:

47H10 Fixed-point theorems
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
47H04 Set-valued operators
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References:

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