A note on best proximity point theorems under weak \(P\)-property. (English) Zbl 1478.54036

Summary: In the very recent paper of A. Abkar and M. Gabeleh [Abstr. Appl. Anal. 2013, Article ID 189567, 3 p. (2013; Zbl 1297.54076)], by using the notion of \(P\)-property, it was proved that some late results about the existence and uniqueness of best proximity points can be obtained from the versions of associated existing results in the fixed point theory. Along the same line, in this paper, we prove that these results can be obtained under a weaker condition, namely, weak \(P\)-property.


54H25 Fixed-point and coincidence theorems (topological aspects)
47H10 Fixed-point theorems
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