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Fixed points of a new type of contractive mappings and multifunctions. (English) Zbl 1340.54053
Extending the results of [B. Samet, C. Vetro, and P. Vetro, Nonlinear Anal., Theory Methods Appl. 75, No. 4, 2154–2165 (2012; Zbl 1242.54027)], the authors introduce notions of \(\alpha\)-\(\psi\)-\(\xi\)-contractive selfmaps and \(\beta\)-\(\psi\)-\(\xi\)-contractive and \(\beta\)-admissible multifunctions in metric spaces and deduce some respective fixed point results.

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