The Schauder fixed point theorem in geodesic spaces. (English) Zbl 1305.54047
Summary: We give a direct proof of Schauder’s fixed point theorem in the setting of geodesic metric spaces, generalizing the classical Schauder’s theorem and improving a recent version of this theorem in \(\mathrm{CAT}(\kappa)\) spaces. As an application we prove an existence result for a variational inequality in the setting of \(\mathrm{CAT}(\kappa)\) spaces.
MSC:
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
Keywords:
fixed point; geodesic spaces; hyperbolic spaces; Leray-Schauder condition; variational inequalityReferences:
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