Fixed points for multivalued mappings in \(b\)-metric spaces. (English) Zbl 1351.54024

Summary: In our previous paper [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 4, 2154–2165 (2012; Zbl 1242.54027)], we introduced the notion of \(\alpha\)-\(\psi\)-contractive mapping and gave sufficient conditions for the existence of fixed points for this class of mappings. The purpose of this paper is to study the existence of fixed points for multivalued mappings, under an \(\alpha\)-\(\psi\)-contractive condition of Ćirić type, in the setting of complete \(b\)-metric spaces. An application to integral equation is given.


54H25 Fixed-point and coincidence theorems (topological aspects)
54C60 Set-valued maps in general topology
54E40 Special maps on metric spaces


Zbl 1242.54027
Full Text: DOI


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