IDEAS home Printed from https://ideas.repec.org/a/hin/ijanal/827862.html
   My bibliography  Save this article

Best Proximity Point Results in Complex Valued Metric Spaces

Author

Listed:
  • Binayak S. Choudhury
  • Nikhilesh Metiya
  • Pranati Maity

Abstract

We introduce the concept of proximity points for nonself-mappings between two subsets of a complex valued metric space which is a recently introduced extension of metric spaces obtained by allowing the metric function to assume values from the field of complex numbers. We apply this concept to obtain the minimum distance between two subsets of the complex valued metric spaces. We treat the problem as that of finding the global optimal solution of a fixed point equation although the exact solution does not in general exist. We also define and use the concept of P-property in such spaces. Our results are illustrated with examples.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:ijanal:827862
    DOI: 10.1155/2014/827862
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/ANALYSIS/2014/827862.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/ANALYSIS/2014/827862.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2014/827862?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. S. Sadiq Basha, 2011. "Best Proximity Points: Optimal Solutions," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 210-216, October.
    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Bessem Samet, 2013. "Some Results on Best Proximity Points," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 281-291, October.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.

    More about this item

    Statistics

    Access and download statistics

    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:hin:ijanal:827862. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.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.