IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2023i1p121-d1310289.html
   My bibliography  Save this article

Fixed Point Results for Hybrid Rational Contractions under a New Compatible Condition with an Application

Author

Listed:
  • Xiaolan Liu

    (College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China
    Artificial Intelligence Key Laboratory of Sichuan Province, Zigong 643000, China
    South Sichuan Center for Applied Mathematics, Zigong 643000, China)

  • Mi Zhou

    (School of Science and Techology, University of Sanya, Sanya 572022, China
    Center for Mathematical Reaserch, University of Sanya, Sanya 572022, China
    Academician Guoliang Chen Team Innovation Center, University of Sanya, Sanya 572022, China
    Academician Chunming Rong Workstation, University of Sanya, Sanya 572022, China)

  • Arslan Hojat Ansari

    (Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj 6915136111, Iran
    Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, Pretoria 0204, South Africa)

  • Naeem Saleem

    (Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, Pretoria 0204, South Africa
    Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan)

  • Mukesh Kumar Jain

    (Jawahar Navodaya Vidyalaya, Udalguri 784509, India)

Abstract

In this scholarly discourse, we present proof of the existence of unique fixed points in b -metric spaces for hybrid rational contractions. Moreover, we establish a common fixed point theorem for four self-mappings, assuming S -compatibility for two pairs of self-mappings within the framework of b -metric spaces. As a practical demonstration of the aforementioned results, we apply them to a type of integral equation and derive a theorem that guarantees the existence of solutions.

Suggested Citation

  • 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 1-16, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2023:i:1:p:121-:d:1310289
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/1/121/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/1/121/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Erdal Karapınar & Andreea Fulga, 2019. "New Hybrid Contractions on b -Metric Spaces," Mathematics, MDPI, vol. 7(7), pages 1-15, June.
    2. Mi Zhou & Xiao-Lan Liu & Arslan Hojat Ansari & Mukesh Kumar Jain & Jia Deng & Naeem Saleem, 2021. "Common Fixed Point Theorems via Inverse Ck− Class Functions in Metric Spaces," Journal of Mathematics, Hindawi, vol. 2021, pages 1-25, April.
    3. Gerald Jungck, 1986. "Compatible mappings and common fixed points," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 9, pages 1-9, January.
    4. Mohammad Ali Alghamdi & Stojan Radenović & Naseer Shahzad, 2012. "On Some Generalizations of Commuting Mappings," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-6, 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. 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.
    2. Mohammed Shehu Shagari & Maha Noorwali & Akbar Azam, 2023. "Hybrid Fixed Point Theorems of Fuzzy Soft Set-Valued Maps with Applications in Integral Inclusions and Decision Making," Mathematics, MDPI, vol. 11(6), pages 1-20, March.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Sharma, Sushil & Deshpande, Bhavana, 2009. "Common fixed point theorems for finite number of mappings without continuity and compatibility on intuitionistic fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2242-2256.
    16. 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).
    17. Rizwan Anjum & Andreea Fulga & Muhammad Waqar Akram, 2023. "Applications to Solving Variational Inequality Problems via MR-Kannan Type Interpolative Contractions," Mathematics, MDPI, vol. 11(22), pages 1-11, November.
    18. Watchareepan Atiponrat & Pariwate Varnakovida & Pharunyou Chanthorn & Teeranush Suebcharoen & Phakdi Charoensawan, 2023. "Common Fixed Point Theorems for Novel Admissible Contraction with Applications in Fractional and Ordinary Differential Equations," Mathematics, MDPI, vol. 11(15), pages 1-20, August.
    19. R. K. Bisht, 2012. "Common Fixed Points of Generalized Meir-Keeler Type Condition and Nonexpansive Mappings," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-12, July.
    20. Abd EL-Monsef, M.E. & Abu-Donia, H.M. & Abd-Rabou, Kh., 2009. "New types of common fixed point theorems in 2-metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1435-1441.

    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:12:y:2023:i:1:p:121-:d:1310289. 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.