Coincidence Point, Best Approximation, and Best Proximity Theorems for Condensing Set-Valued Maps in Hyperconvex Metric Spaces
نویسندگان
چکیده
The best approximation problem in a hyperconvex metric space consists of finding conditions for given set-valued mappings F andG and a setX such that there is a point x0 ∈ X satisfying d G x0 , F x0 ≤ d x, F x0 for x ∈ X. When G I, the identity mapping, and when the set X is compact, best approximation theorems for mappings in hyperconvex metric spaces are given for the single-valued case in 1–4 , for the set-valued case in 1, 3, 5–9 . Some results for condensing set-valued maps were given in 2 . Given subsets A, B, set-valued mappings F : A B, and G : A A the best proximity problem consists of finding conditions on F, G, A, and B implying that there is a point x0 ∈ A such that d G x0 , F x0 d A,B . Then G x0 , F x0 is called a best proximity pair, see 2, 10 . ForA, B nonempty subsets of a metric spaceM, we define the following sets
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Best proximity pair and coincidence point theorems for nonexpansive set-valued maps in Hilbert spaces
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