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Convergence and Best Proximity Points for Generalized Contraction Pairs

Author

Listed:
  • Slah Sahmim

    (Department of Mathematics and Statistics, College of Sciences, King Faisal University, P.O. Box 400, Hafouf 31982, Saudi Arabia)

  • Abdelbasset Felhi

    (Department of Mathematics and Physics Preparatory Engineering Institute, Carthage University, Bizerte 7021, Tunisia)

  • Hassen Aydi

    (Department of Mathematics, College of Education of Jubail, Imam Abdulrahman Bin Faisal University, P.O. 12020, Industrial Jubail 31961, Saudi Arabia)

Abstract

This paper is devoted to studying the existence of best proximity points and convergence for a class of generalized contraction pairs by using the concept of proximally-complete pairs and proximally-complete semi-sharp proximinal pairs. The obtained results are generalizations of the result of Sadiq Basha (Basha, S., Best proximity points: global optimal approximate solutions, J. Glob. Optim. 2011 , 49 , 15–21) As an application, we give a result for nonexpansive mappings in normed vector spaces.

Suggested Citation

  • Slah Sahmim & Abdelbasset Felhi & Hassen Aydi, 2019. "Convergence and Best Proximity Points for Generalized Contraction Pairs," Mathematics, MDPI, vol. 7(2), pages 1-12, February.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:2:p:176-:d:206060
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    References listed on IDEAS

    as
    1. 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.
    2. S. Sadiq Basha, 2011. "Best proximity points: global optimal approximate solutions," Journal of Global Optimization, Springer, vol. 49(1), pages 15-21, January.
    3. N. Shahzad & S. Sadiq Basha & R. Jeyaraj, 2011. "Common Best Proximity Points: Global Optimal Solutions," Journal of Optimization Theory and Applications, Springer, vol. 148(1), pages 69-78, January.
    4. S. Sadiq Basha, 2011. "Best Proximity Points: Optimal Solutions," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 210-216, October.
    5. Rafael Espínola & G. Sankara Raju Kosuru & P. Veeramani, 2015. "Pythagorean Property and Best-Proximity Point Theorems," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 534-550, February.
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