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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
##### Keywords:
fixed point; directed graph; metric space; set valued mapping
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##### References:
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