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Best Proximity Points for Cyclic Mappings in Ordered Metric Spaces

Author

Listed:
  • A. Abkar

    (Imam Khomeini International University)

  • M. Gabeleh

    (Imam Khomeini International University)

Abstract

In this paper, we consider a cyclic mapping on a partially ordered complete metric space. We prove some fixed point theorems, as well as some theorems on the existence and convergence of best proximity points.

Suggested Citation

  • A. Abkar & M. Gabeleh, 2011. "Best Proximity Points for Cyclic Mappings in Ordered Metric Spaces," Journal of Optimization Theory and Applications, Springer, vol. 151(2), pages 418-424, November.
    • Handle: RePEc:spr:joptap:v:151:y:2011:i:2:d:10.1007_s10957-011-9818-2
    DOI: 10.1007/s10957-011-9818-2
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    Citations

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    Cited by:

    1. A. Abkar & M. Gabeleh, 2012. "Global Optimal Solutions of Noncyclic Mappings in Metric Spaces," Journal of Optimization Theory and Applications, Springer, vol. 153(2), pages 298-305, May.
    2. Chirasak Mongkolkeha & Poom Kumam, 2012. "Best Proximity Point Theorems for Generalized Cyclic Contractions in Ordered Metric Spaces," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 215-226, October.
    3. Muhammad Zahid & Fahim Ud Din & Mudasir Younis & Haroon Ahmad & Mahpeyker Öztürk, 2024. "Some Results on Multivalued Proximal Contractions with Application to Integral Equation," Mathematics, MDPI, vol. 12(22), pages 1-21, November.
    4. Naeem Saleem & Jelena Vujaković & Wali Ullah Baloch & Stojan Radenović, 2019. "Coincidence Point Results for Multivalued Suzuki Type Mappings Using θ -Contraction in b -Metric Spaces," Mathematics, MDPI, vol. 7(11), pages 1-21, October.
    5. Muhammad Usman Ali & Misbah Farheen & Tayyab Kamran & Georgeta Maniu, 2019. "Prešić Type Nonself Operators and Related Best Proximity Results," Mathematics, MDPI, vol. 7(5), pages 1-12, April.

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