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New fixed point theorems for set-valued contractions in \(b\)-metric spaces. (English) Zbl 1383.54048
Summary: In this paper, we indicate a way to generalize a series of fixed point results in the framework of \(b\)-metric spaces and we exemplify it by extending Nadler’s contraction principle for set-valued functions (see [S. B. Nadler jun., Pac. J. Math. 30, 475–488 (1969; Zbl 0187.45002)]) and a fixed point theorem for set-valued quasi-contraction functions due to H. Aydi et al. [Fixed Point Theory Appl. 2012, Paper No. 88, 8 p. (2012; Zbl 06215370)].

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
47H10 Fixed-point theorems
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