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Some results on fixed points of \({\alpha}\)-\(\psi\)-Ćirić generalized multifunctions. (English) Zbl 1423.54090
Summary: In [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 4, 2154–2165 (2012; Zbl 1242.54027)], B. Samet et al. introduced \({\alpha}\)-\(\psi\)-contractive mappings and gave some results on a fixed point of the mappings. In fact, their technique generalized some ordered fixed point results (see [H. Alikhani et al., Filomat 27, No. 7, 1315–1319 (2013; Zbl 1340.54053); Samet et al., loc. cit.]. By using the main idea of Samet et al. [loc. cit.], we give some new results for \({\alpha}\)-\(\psi\)-Ćirić generalized multifunctions and some related self-maps. Also, we give an affirmative answer to a recent open problem which was raised by R. H. Haghi et al. [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 5, 1799–1803 (2011; Zbl 1251.54045)].

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