IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i2p176-d206060.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/2/176/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/7/2/176/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. S. Sadiq Basha, 2011. "Best Proximity Points: Optimal Solutions," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 210-216, October.
    3. 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.
    4. S. Sadiq Basha, 2011. "Best proximity points: global optimal approximate solutions," Journal of Global Optimization, Springer, vol. 49(1), pages 15-21, January.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Moosa Gabeleh, 2013. "Proximal Weakly Contractive and Proximal Nonexpansive Non-self-Mappings in Metric and Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 158(2), pages 615-625, August.
    2. 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.
    3. Ali Abkar & Narges Moezzifar & Azizollah Azizi, 2016. "Best Proximity Point Theorems in Partially Ordered b -Quasi Metric Spaces," Mathematics, MDPI, vol. 4(4), pages 1-16, November.
    4. Bessem Samet, 2013. "Some Results on Best Proximity Points," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 281-291, October.
    5. S. Sadiq Basha & N. Shahzad & R. Jeyaraj, 2013. "Best proximity point theorems: exposition of a significant non-linear programming problem," Journal of Global Optimization, Springer, vol. 56(4), pages 1699-1705, August.
    6. Hind Alamri & Nawab Hussain & Ishak Altun, 2023. "Proximity Point Results for Generalized p -Cyclic Reich Contractions: An Application to Solving Integral Equations," Mathematics, MDPI, vol. 11(23), pages 1-25, November.
    7. Moosa Gabeleh, 2015. "Best Proximity Point Theorems via Proximal Non-self Mappings," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 565-576, February.
    8. Naeem Saleem & Mujahid Abbas & Manuel De la Sen, 2019. "Optimal Approximate Solution of Coincidence Point Equations in Fuzzy Metric Spaces," Mathematics, MDPI, vol. 7(4), pages 1-13, April.
    9. S. Sadiq Basha, 2011. "Best Proximity Points: Optimal Solutions," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 210-216, October.
    10. V. Sankar Raj & A. Anthony Eldred, 2014. "A Characterization of Strictly Convex Spaces and Applications," Journal of Optimization Theory and Applications, Springer, vol. 160(2), pages 703-710, February.
    11. Poom Kumam & Chirasak Mongkolkeha, 2019. "Global Optimization for Quasi-Noncyclic Relatively Nonexpansive Mappings with Application to Analytic Complex Functions," Mathematics, MDPI, vol. 7(1), pages 1-8, January.
    12. S. Sadiq Basha, 2014. "Best proximity point theorems: unriddling a special nonlinear programming problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 543-553, July.
    13. Hakan Sahin, 2022. "A New Best Proximity Point Result with an Application to Nonlinear Fredholm Integral Equations," Mathematics, MDPI, vol. 10(4), pages 1-14, February.
    14. Victoria Olisama & Johnson Olaleru & Hudson Akewe, 2017. "Best Proximity Point Results for Some Contractive Mappings in Uniform Spaces," International Journal of Analysis, Hindawi, vol. 2017, pages 1-8, April.
    15. Binayak S. Choudhury & Nikhilesh Metiya & Pranati Maity, 2014. "Best Proximity Point Results in Complex Valued Metric Spaces," International Journal of Analysis, Hindawi, vol. 2014, pages 1-6, August.
    16. Manuel De la Sen & Mujahid Abbas & Naeem Saleem, 2017. "On Optimal Fuzzy Best Proximity Coincidence Points of Proximal Contractions Involving Cyclic Mappings in Non-Archimedean Fuzzy Metric Spaces," Mathematics, MDPI, vol. 5(2), pages 1-20, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:7:y:2019:i:2:p:176-:d:206060. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.