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Fixed point theorems for nonself Bianchini type contractions in Banach spaces endowed with a graph. (English) Zbl 1463.47160

Summary: In this paper we present an extension of fixed point theorem for self mappings on metric spaces endowed with a graph and which satisfies a Bianchini contraction condition. We establish conditions which ensure the existence of fixed point for a non-self Bianchini contractions \(T:K\subset X\to X\) that satisfy Rothe’s boundary condition \(T(\partial K)\subset K\).

MSC:

47H10 Fixed-point theorems
47H08 Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc.
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
54H25 Fixed-point and coincidence theorems (topological aspects)
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