IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i21p4455-d1269029.html
   My bibliography  Save this article

Best Approximation of Fixed-Point Results for Branciari Contraction of Integral Type on Generalized Modular Metric Space

Author

Listed:
  • Nesrin Manav Tatar

    (Department of Mathematics, Erzincan Binali Yildirim University, Erzincan 24002, Turkey)

  • Ravi P. Agarwal

    (Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363-8202, USA)

Abstract

In the realm of generalized modular metric spaces, we substantiate the validity of fixed-point theorems with Branciari contractions. This paper expands and broadens the original theorems in this context. Subsequently, by building upon this foundation, we explore various integral contractions to identify and characterize fixed points within this context. To highlight the practical implications of our work, we introduce the concept of the best proximity pair, thereby culminating in the best approximation theorem. We apply this theoretical construct to a specific example—one that is guided by the best approximation method described in prior research.

Suggested Citation

  • Nesrin Manav Tatar & Ravi P. Agarwal, 2023. "Best Approximation of Fixed-Point Results for Branciari Contraction of Integral Type on Generalized Modular Metric Space," Mathematics, MDPI, vol. 11(21), pages 1-15, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:21:p:4455-:d:1269029
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/21/4455/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/21/4455/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. A. Branciari, 2002. "A fixed point theorem for mappings satisfying a general contractive condition of integral type," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 29, pages 1-6, January.
    2. Naveen Mani & Amit Sharma & Rahul Shukla & Jozef Banas, 2023. "Fixed Point Results via Real-Valued Function Satisfying Integral Type Rational Contraction," Abstract and Applied Analysis, Hindawi, vol. 2023, pages 1-6, January.
    3. P. Vijayaraju & B. E. Rhoades & R. Mohanraj, 2005. "A fixed point theorem for a pair of maps satisfying a general contractive condition of integral type," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-6, January.
    4. Gerald Jungck, 1986. "Compatible mappings and common fixed points," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 9, pages 1-9, January.
    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. J. R. Morales & E. M. Rojas, 2012. "Some Generalizations of Jungck's Fixed Point Theorem," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-19, November.
    2. Shatanawi, Wasfi, 2012. "Some fixed point results for a generalized ψ-weak contraction mappings in orbitally metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 45(4), pages 520-526.
    3. Samet, Bessem & Vetro, Calogero, 2011. "Berinde mappings in orbitally complete metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 44(12), pages 1075-1079.
    4. Ghosh, S.K. & Nahak, C., 2020. "An extension of Lakzian-Rhoades results in the structure of ordered b-metric spaces via wt-distance with an application," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    5. Lakzian, Hossein & Rhoades, B.E., 2019. "Some fixed point theorems using weaker Meir–Keeler function in metric spaces with w−distance," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 18-25.
    6. Budi Nurwahyu, 2019. "Common Fixed Point Theorems on Generalized Ratio Contraction Mapping in Extended Rectangular b -Metric Spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2019, pages 1-14, December.
    7. Manish Jain & Neetu Gupta & Sanjay Kumar, 2014. "Coupled Fixed Point Theorems for ( )-Contractive Mixed Monotone Mappings in Partially Ordered Metric Spaces and Applications," International Journal of Analysis, Hindawi, vol. 2014, pages 1-9, March.
    8. Rqeeb Gubran & Mohammad Imdad, 2016. "Results on Coincidence and Common Fixed Points for (ψ,φ) g -Generalized Weakly Contractive Mappings in Ordered Metric Spaces," Mathematics, MDPI, vol. 4(4), pages 1-13, December.
    9. Cho, Yeol Je & Sedghi, Shaban & Shobe, Nabi, 2009. "Generalized fixed point theorems for compatible mappings with some types in fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2233-2244.
    10. Muhammad Shoaib & Muhammad Sarwar, 2016. "Multivalued Fixed Point Theorems for Generalized Contractions and Their Applications," Journal of Mathematics, Hindawi, vol. 2016, pages 1-8, October.
    11. Zoran D. Mitrović & Hassen Aydi & Nawab Hussain & Aiman Mukheimer, 2019. "Reich, Jungck, and Berinde Common Fixed Point Results on ℱ-Metric Spaces and an Application," Mathematics, MDPI, vol. 7(5), pages 1-10, April.
    12. Deshpande, Bhavana, 2009. "Fixed point and (DS)-weak commutativity condition in intuitionistic fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2722-2728.
    13. Mohammad Imdad & Sunny Chauhan, 2013. "Employing Common Limit Range Property to Prove Unified Metrical Common Fixed Point Theorems," International Journal of Analysis, Hindawi, vol. 2013, pages 1-10, May.
    14. 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.
    15. Xiaolan Liu & Mi Zhou & Arslan Hojat Ansari & Naeem Saleem & Mukesh Kumar Jain, 2023. "Fixed Point Results for Hybrid Rational Contractions under a New Compatible Condition with an Application," Mathematics, MDPI, vol. 12(1), pages 1, December.
    16. Piyachat Borisut & Poom Kumam & Vishal Gupta & Naveen Mani, 2019. "Generalized ( ψ , α , β )—Weak Contractions for Initial Value Problems," Mathematics, MDPI, vol. 7(3), pages 1-14, March.
    17. Muhammad Shoaib & Muhammad Sarwar & Sultan Hussain & Gohar Ali, 2017. "Existence and Uniqueness of Common Fixed Point for Mappings Satisfying Integral Type Contractive Conditions in G-Metric Spaces," Matrix Science Mathematic (MSMK), Zibeline International Publishing, vol. 1(1), pages 1-8, January.
    18. Hemant Kumar Nashine & Hassen Aydi, 2012. "Generalized Altering Distances and Common Fixed Points in Ordered Metric Spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-23, July.
    19. Zoran D. Mitrović & Abasalt Bodaghi & Ahmad Aloqaily & Nabil Mlaiki & Reny George, 2023. "New Versions of Some Results on Fixed Points in b -Metric Spaces," Mathematics, MDPI, vol. 11(5), pages 1-9, February.
    20. Mustafa Mudhesh & Aftab Hussain & Muhammad Arshad & Hamed Alsulami, 2023. "A Contemporary Approach of Integral Khan-Type Multivalued Contractions with Generalized Dynamic Process and an Application," Mathematics, MDPI, vol. 11(20), pages 1-18, October.

    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:21:p:4455-:d:1269029. 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.