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Some fixed point results on a metric space with a graph. (English) Zbl 1237.54042
The main results of this paper (Theorems 2.1–2.4) deal with the stability (not explicitly called so) for the Picard iteration associated to \(G\)-contractions or \(G\)-nonexpansive mappings defined on a metric space endowed with a graph \(G\).

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces
05C63 Infinite graphs
47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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