Horvat-Marc, Andrei; Balog, Laszlo Fixed point theorems for nonself Bianchini type contractions in Banach spaces endowed with a graph. (English) Zbl 1463.47160 Creat. Math. Inform. 27, No. 1, 37-48 (2018). 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 \(T(\partial K)\subset K\). Cited in 1 Document 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) Keywords:fixed point theorem; boundary condition; Bianchini contraction PDFBibTeX XMLCite \textit{A. Horvat-Marc} and \textit{L. Balog}, Creat. Math. Inform. 27, No. 1, 37--48 (2018; Zbl 1463.47160)