IDEAS home Printed from https://ideas.repec.org/a/wly/jnljam/v2014y2014i1n150941.html

Best Proximity Point for Generalized Proximal Weak Contractions in Complete Metric Space

Author

Listed:
  • Erdal Karapınar
  • V. Pragadeeswarar
  • M. Marudai

Abstract

We introduce a new class of nonself‐mappings, generalized proximal weak contraction mappings, and prove the existence and uniqueness of best proximity point for such mappings in the context of complete metric spaces. Moreover, we state an algorithm to determine such an optimal approximate solution designed as a best proximity point. We establish also an example to illustrate our main results. Our result provides an extension of the related results in the literature.

Suggested Citation

  • Erdal Karapınar & V. Pragadeeswarar & M. Marudai, 2014. "Best Proximity Point for Generalized Proximal Weak Contractions in Complete Metric Space," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:150941
    DOI: 10.1155/2014/150941
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2014/150941
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2014/150941?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. Mohamed Jleli & Erdal Karapınar & Bessem Samet, 2012. "Fixed Point Results for Almost Generalized Cyclic -Weak Contractive Type Mappings with Applications," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-17, August.
    2. Mohamed Jleli & Erdal Karapınar & Bessem Samet, 2012. "Fixed Point Results for Almost Generalized Cyclic (ψ, φ)‐Weak Contractive Type Mappings with Applications," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. Erdal Karapınar & I. Savas Yuce, 2012. "Fixed Point Theory for Cyclic Generalized Weak ϕ‐Contraction on Partial Metric Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. V. Pragadeeswarar & M. Marudai & P. Kumam & K. Sitthithakerngkiet, 2014. "The Existence and Uniqueness of Coupled Best Proximity Point for Proximally Coupled Contraction in a Complete Ordered Metric Space," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. V. Pragadeeswarar & M. Marudai, 2015. "Best Proximity Points for Generalized Proximal Weak Contractions Satisfying Rational Expression on Ordered Metric Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2015(1).

    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. Chiming Chen & Ing-Jer Lin, 2013. "Common Fixed Points of Generalized Cyclic Meir‐Keeler‐Type Contractions in Partially Ordered Metric Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Hassen Aydi & Erdal Karapınar & Bessem Samet, 2012. "Fixed Point Theorems for Various Classes of Cyclic Mappings," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    3. Mohamed Jleli & Erdal Karapınar & Bessem Samet, 2012. "Best Proximity Point Results for MK‐Proximal Contractions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    4. Savita Rathee & Anil Kumar & Kenan Tas, 2014. "Invariant Approximation Results via Common Fixed Point Theorems for Generalized Weak Contraction Maps," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    5. Hemant Kumar Nashine & Zoran Kadelburg, 2013. "Cyclic Contractions and Fixed Point Results via Control Functions on Partial Metric Spaces," International Journal of Analysis, Hindawi, vol. 2013, pages 1-9, February.
    6. Chi-Ming Chen & Jin-Chirng Lee & Chao-Hung Chen, 2013. "Fixed Point Theory of Weak Contractions in Partially Ordered Metric Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).

    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:wly:jnljam:v:2014:y:2014:i:1:n:150941. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4185 .

    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.