Best Proximity Point Theorems via Proximal Non-self Mappings

Moosa Gabeleh ()
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Moosa Gabeleh: Ayatollah Boroujerdi University

Journal of Optimization Theory and Applications, 2015, vol. 164, issue 2, No 10, 565-576

Abstract: Abstract We prove a best proximity point theorem for proximal generalized contractive type mappings in metric spaces, which is a generalization of recent best proximity point theorems and some famous fixed point theorems due to Berinde and Suzuki. We also introduce a new class of proximal non-self mappings and obtain sufficient conditions, which ensure the existence of a best proximity point. Moreover, we define algorithms and prove that they find a best proximity point for these classes of non-self mappings in the setting of metric and Banach spaces.

Keywords: Best proximity point; Berinde weak proximal contraction; Proximal generalized nonexpansive; Approximatively compactness; 47H10; 47H09 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10957-014-0585-8

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