IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i6p1277-d1089523.html

Relational Contractions Involving (c)-Comparison Functions with Applications to Boundary Value Problems

Author

Listed:
  • Ebrahem Ateatullah Algehyne

    (Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia)

  • Musaad Sabih Aldhabani

    (Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia)

  • Faizan Ahmad Khan

    (Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia)

Abstract

After the introduction of Alam–Imdad’s relation-theoretic contraction principle, the field of metric fixed point theory has attracted much attention. A number of fixed point theorems in the context of relational metric space employing various types of contractions has been appeared during the last seven years. In this manuscript, one proved a metrical fixed point theorem for ϕ -contraction involving (c)-comparison functions employing an amorphous relation. The result proved in this paper refines, modifies, unifies and sharpens several existing fixed point results. We also constructed an example in order to attest the credibility of our results. Finally, we applied our result to establish the existence and uniqueness of solution of certain periodic boundary value problem.

Suggested Citation

  • Ebrahem Ateatullah Algehyne & Musaad Sabih Aldhabani & Faizan Ahmad Khan, 2023. "Relational Contractions Involving (c)-Comparison Functions with Applications to Boundary Value Problems," Mathematics, MDPI, vol. 11(6), pages 1-11, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1277-:d:1089523
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/6/1277/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/6/1277/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Nawab Hussain & Zoran Kadelburg & Stojan Radenović & Falleh Al-Solamy, 2012. "Comparison Functions and Fixed Point Results in Partial Metric Spaces," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-15, June.
    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. Khursheed J. Ansari & Salvatore Sessa & Aftab Alam, 2023. "A Class of Relational Functional Contractions with Applications to Nonlinear Integral Equations," Mathematics, MDPI, vol. 11(15), pages 1-11, August.
    2. Manuel De la Sen & Asier Ibeas & Aitor J. Garrido & Izaskun Garrido, 2025. "Fixed Points of Self-Mappings with Jumping Effects: Application to Stability of a Class of Impulsive Dynamic Systems," Mathematics, MDPI, vol. 13(7), pages 1-42, March.
    3. Esmail Alshaban & Adel Alatawi & Fahad M. Alamrani & Ahmed Alamer & Naif N. Alrshidi & Faizan Ahmad Khan, 2025. "Nonlinear Almost Contractions of Pant Type Under Binary Relations with an Application to Boundary Value Problems," Mathematics, MDPI, vol. 13(6), pages 1-16, March.

    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. Erdal Karapınar & Ravi P. Agarwal & Seher Sultan Yeşilkaya & Chao Wang, 2022. "Fixed-Point Results for Meir–Keeler Type Contractions in Partial Metric Spaces: A Survey," Mathematics, MDPI, vol. 10(17), pages 1-76, August.
    2. Mujahid Abbas & Hassen Aydi & Stojan Radenović, 2012. "Fixed Point of -Hardy-Rogers Contractive Mappings in Partially Ordered Partial Metric Spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-11, September.
    3. N. Hussain & E. Karapınar & S. Sedghi & N. Shobkolaei & S. Firouzian, 2014. "Cyclic (ϕ)‐Contractions in Uniform Spaces and Related Fixed Point Results," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    4. N. Hussain & S. Al-Mezel & P. Salimi, 2013. "Fixed Points for ψ‐Graphic Contractions with Application to Integral Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    5. M. A. Kutbi & Jamshaid Ahmad & Nawab Hussain & Muhammad Arshad, 2013. "Common Fixed Point Results for Mappings with Rational Expressions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    6. Ondrej Rozinek & Monika Borkovcova, 2023. "Theorems for Boyd–Wong Contraction Mappings on Similarity Spaces," Mathematics, MDPI, vol. 11(20), pages 1-10, October.
    7. Monica-Felicia Bota & Erdal Karapınar & Oana Mleşniţe, 2013. "Ulam‐Hyers Stability Results for Fixed Point Problems via α‐ψ‐Contractive Mapping in (b)‐Metric Space," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    8. Abd Ghafur Bin Ahmad & Zaid Mohammed Fadail & Vesna Ćojbašić Rajić & Stojan Radenović, 2012. "Nonlinear Contractions in 0‐Complete Partial Metric Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    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:gam:jmathe:v:11:y:2023:i:6:p:1277-:d:1089523. 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 The email address of this maintainer does not seem to be valid anymore. Please ask MDPI Indexing Manager to update the entry or send us the correct address (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.