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Best proximity point for \(\alpha\)-\(\psi\)-proximal contractive multimaps. (English) Zbl 1469.54045

Summary: We extend the notions of \(\alpha\)-\(\psi\)-proximal contraction and \(\alpha\)-proximal admissibility to multivalued maps and then using these notions we obtain some best proximity point theorems for multivalued mappings. Our results extend some recent results by M. Jleli and B. Samet and those contained therein [Bull. Sci. Math. 137, No. 8, 977–995 (2013; Zbl 1290.41024)]. Some examples are constructed to show the generality of our results.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54C60 Set-valued maps in general topology

Citations:

Zbl 1290.41024
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References:

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