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The contraction principle for set valued mappings on a metric space with a graph. (English) Zbl 1201.54029
Summary: Let (X,d) be a metric space and F:XX be a set valued mapping. We obtain sufficient conditions for the existence of a fixed point of the mapping F in the metric space X endowed with a graph G such that the set V(G) of vertices of G coincides with X and the set of edges of G is E(G)={(x,y):(x,y)X×X}.
MSC:
54H25Fixed-point and coincidence theorems in topological spaces
65J15Equations with nonlinear operators (numerical methods)
47H10Fixed point theorems for nonlinear operators on topological linear spaces
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