Journal of Optimization Theory and Applications

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

Best Proximity Point Theorems via Proximal Non-self Mappings

Article
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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 

Mathematics Subject Classification

47H10 47H09 
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Notes

Acknowledgments

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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