Affiliation:
1. Department of Mathematics, The Technion—Israel Institute of Technology, Haifa 32000, Israel
Abstract
It is known that a strict contraction on a complete metric space with a graph possesses a fixed point. In the present paper, we show that this property holds for single valued and set-valued self-mappings of metric spaces with graphs that are of the contractive type. We also show the convergence of iterates of these mappings to fixed points. In particular, our results are true for metric spaces with symmetric graphs.
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