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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 \(F:X\rightsquigarrow X\) 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 \(E(G)=\{(x,y):(x,y)\in X\times X\}\).

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
65J15 Numerical solutions to equations with nonlinear operators
47H10 Fixed-point theorems
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