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Best Proximity Point Theorems for Generalized \(\alpha \)-\(\psi \)-Proximal Contractions

  • Muhammad Usman Ali
  • Arslan Hojat Ansari
  • Konrawut Khammahawong
  • Poom Kumam
Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 760)

Abstract

In this paper, we introduce a new generalization of multi-valued \(\alpha \)-\(\psi \)-proximal contraction and prove some best proximity point theorems for such mappings on complete metric spaces. An example is also constructed to show the generality of our results.

Keywords

Best proximity point \(\alpha \)-\(\psi \)-proximal contraction \((h , F , \alpha , \mu , \psi )\)-proximal contraction \((h , F , \alpha , \beta , \mu , \psi )\)-proximal contraction 

Mathematics Subject Classification:

Primary 47H10 Secondary 54H25. 

Notes

Acknowledgements

This project was supported by the Theoretical and Computational Science (TaCS) Center under Computational and Applied Science for Smart Innovation Cluster (CLASSIC), Faculty of Science, KMUTT. The third author would like to thank the Research Professional Development Project Under the Science Achievement Scholarship of Thailand (SAST) for financial support.

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Muhammad Usman Ali
    • 1
  • Arslan Hojat Ansari
    • 2
  • Konrawut Khammahawong
    • 3
    • 4
  • Poom Kumam
    • 3
    • 4
  1. 1.Department of MathematicsCOMSATS Institute of Information TechnologyAttockPakistan
  2. 2.Department of MathematicsKaraj Branch, Islamic Azad UniversityKarajIran
  3. 3.KMUTT-Fixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of ScienceKing Mongkut’s University of Technology Thonburi (KMUTT)BangkokThailand
  4. 4.KMUTT-Fixed Point Theory and Applications Research Group (KMUTT-FPTA), Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of ScienceKing Mongkut’s University of Technology Thonburi (KMUTT)BangkokThailand

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