Journal of Optimization Theory and Applications

, Volume 164, Issue 2, pp 565–576 | Cite as

Best Proximity Point Theorems via Proximal Non-self Mappings

  • Moosa Gabeleh


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.


Best proximity point Berinde weak proximal contraction Proximal generalized nonexpansive Approximatively compactness 

Mathematics Subject Classification

47H10 47H09 



The author thanks the referees for their valuable suggestions.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of MathematicsAyatollah Boroujerdi UniversityBoroujerdIran

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