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On fixed points of \({\alpha}\)-\({\psi}\)-contractive multifunctions. (English) Zbl 1293.54017
Summary: Recently, B. Samet et al. [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 4, 2154–2165 (2012; Zbl 1242.54027)] introduced the notion of \({\alpha}\)-\({\psi}\)-contractive type mappings and established some fixed point theorems in complete metric spaces. In this paper, we introduce the notion of \({\alpha}_*\)-\({\psi}\)-contractive multifunctions and give a fixed point result for these multifunctions. We also obtain a fixed point result for self-maps in complete metric spaces satisfying a contractive condition.

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
54C60 Set-valued maps in general topology
54E40 Special maps on metric spaces
54E50 Complete metric spaces
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