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Best proximity points for \(\psi\)-proximal multi-functions. (English) Zbl 1458.54052

Summary: Best proximity point theorems for self-mappings and multi-functions were investigated with different conditions on spaces and the contractions of mappings. In this paper, we will prove best proximity point theorems for some generalized multi-functions that we call \(\psi\)-proximal multi-functions, which are of two types, \(\psi\)-proximal multi-functions of the first and second kind.

MSC:

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