Best proximity points: global minimization of multivalued non-self mappings. (English) Zbl 1321.90152
Summary: In this article, we give a best proximity point theorem for generalized contractions in metric spaces with appropriate geometric property. We also, give an example which ensures that our result cannot be obtained from a similar result due to A. Amini-Harandi [Optim. Lett. 7, No. 5, 913–921 (2013; Zbl 1277.54029)]. Moreover, we prove a best proximity point theorem for multivalued non-self mappings which generalizes the N. Mizoguchi and W. Takahashi’s fixed point theorem for multivalued mappings [J. Math. Anal. Appl. 141, No. 1, 177–188 (1989; Zbl 0688.54028)].
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