Geodesic
A fixed point theoremfor nonexpansive compact self-mapping
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 68 (2014) no. 1.

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A mapping T from a topological space X to a topological space Y is said to be compact if T(X) is contained in a compact subset of Y . The aim of this paper is to prove the existence of fixed points of a nonexpansive compact self-mapping defined on a closed subset having a contractive jointly continuous family when the underlying space is a metric space. The proved result generalizes and extends several known results on the subject. 
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Narang, T. D. A fixed point theoremfor nonexpansive compact self-mapping. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 68 (2014) no. 1. http://geodesic.mathdoc.fr/item/AUM_2014_68_1_a0/

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