IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i6p1390-d1096033.html
   My bibliography  Save this article

Fuzzy Triple Controlled Metric like Spaces with Applications

Author

Listed:
  • Naeem Saleem

    (Department of Mathematics, University of Management and Technology Lahore, Lahore 54770, Pakistan)

  • Salman Furqan

    (Department of Mathematics, University of Management and Technology Lahore, Lahore 54770, Pakistan)

  • Kinda Abuasbeh

    (Department of Mathematics and Statistics, College of Science, King Faisal University, Hafuaf 31982, Al Ahsa, Saudi Arabia)

  • Muath Awadalla

    (Department of Mathematics and Statistics, College of Science, King Faisal University, Hafuaf 31982, Al Ahsa, Saudi Arabia)

Abstract

In this article, we introduce the concept of a fuzzy triple controlled metric like space in the sense that the self distance may not be equal to one. We have used three functions in our space that generalize fuzzy controlled rectangular, extended fuzzy rectangular, fuzzy b – rectangular and fuzzy rectangular metric like spaces. Various examples are given to justify our definitions and results. As for the topological aspect, we prove a fuzzy triple controlled metric like space is not Hausdorff. We also apply our main result to solve the uniqueness of the solution of a fractional differential equation.

Suggested Citation

  • Naeem Saleem & Salman Furqan & Kinda Abuasbeh & Muath Awadalla, 2023. "Fuzzy Triple Controlled Metric like Spaces with Applications," Mathematics, MDPI, vol. 11(6), pages 1-30, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1390-:d:1096033
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/6/1390/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/6/1390/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hasanen A. Hammad & Praveen Agarwal & Juan L. G. Guirao, 2021. "Applications to Boundary Value Problems and Homotopy Theory via Tripled Fixed Point Techniques in Partially Metric Spaces," Mathematics, MDPI, vol. 9(16), pages 1-22, August.
    2. Liu, Tao, 2022. "Porosity reconstruction based on Biot elastic model of porous media by homotopy perturbation method," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    3. Mohamed M. Mousa & Fahad Alsharari, 2021. "Convergence and Error Estimation of a New Formulation of Homotopy Perturbation Method for Classes of Nonlinear Integral/Integro-Differential Equations," Mathematics, MDPI, vol. 9(18), pages 1-14, September.
    4. Nabil Mlaiki & Hassen Aydi & Nizar Souayah & Thabet Abdeljawad, 2018. "Controlled Metric Type Spaces and the Related Contraction Principle," Mathematics, MDPI, vol. 6(10), pages 1-7, October.
    5. N. Mlaiki & K. Abodayeh & H. Aydi & T. Abdeljawad & M. Abuloha, 2018. "Rectangular Metric-Like Type Spaces and Related Fixed Points," Journal of Mathematics, Hindawi, vol. 2018, pages 1-7, September.
    6. Thabet Abdeljawad & Nabil Mlaiki & Hassen Aydi & Nizar Souayah, 2018. "Double Controlled Metric Type Spaces and Some Fixed Point Results," Mathematics, MDPI, vol. 6(12), pages 1-10, December.
    7. Damian Słota & Agata Chmielowska & Rafał Brociek & Marcin Szczygieł, 2020. "Application of the Homotopy Method for Fractional Inverse Stefan Problem," Energies, MDPI, vol. 13(20), pages 1-14, 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. Hasanen A. Hammad & Mohra Zayed, 2022. "New Generalized Contractions by Employing Two Control Functions and Coupled Fixed-Point Theorems with Applications," Mathematics, MDPI, vol. 10(17), pages 1-18, September.
    2. Abdullah Eqal Al-Mazrooei & Jamshaid Ahmad, 2022. "Fixed Point Results in Controlled Metric Spaces with Applications," Mathematics, MDPI, vol. 10(3), pages 1-15, February.
    3. Amiri, Pari & Afshari, Hojjat, 2022. "Common fixed point results for multi-valued mappings in complex-valued double controlled metric spaces and their applications to the existence of solution of fractional integral inclusion systems," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    4. 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.
    5. Nayab Alamgir & Quanita Kiran & Hassen Aydi & Aiman Mukheimer, 2019. "A Mizoguchi–Takahashi Type Fixed Point Theorem in Complete Extended b -Metric Spaces," Mathematics, MDPI, vol. 7(5), pages 1-15, May.
    6. Thangaraj, C. & Easwaramoorthy, D. & Selmi, Bilel & Chamola, Bhagwati Prasad, 2024. "Generation of fractals via iterated function system of Kannan contractions in controlled metric space," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 222(C), pages 188-198.
    7. Mujahid Abbas & Hira Iqbal & Manuel De la Sen & Khushdil Ahmad, 2021. "Approximation of Fixed Points of Multivalued Generalized ( α , β )-Nonexpansive Mappings in an Ordered CAT(0) Space," Mathematics, MDPI, vol. 9(16), pages 1-21, August.
    8. Vishnu Narayan Mishra & Luis Manuel Sánchez Ruiz & Pragati Gautam & Swapnil Verma, 2020. "Interpolative Reich–Rus–Ćirić and Hardy–Rogers Contraction on Quasi-Partial b-Metric Space and Related Fixed Point Results," Mathematics, MDPI, vol. 8(9), pages 1-11, September.
    9. Hassen Aydi & Chi-Ming Chen & Erdal Karapınar, 2019. "Interpolative Ćirić-Reich-Rus Type Contractions via the Branciari Distance," Mathematics, MDPI, vol. 7(1), pages 1-7, January.
    10. Nabil Mlaiki & Mohammad Asim & Mohammad Imdad, 2020. "C *-Algebra Valued Partial b -Metric Spaces and Fixed Point Results with an Application," Mathematics, MDPI, vol. 8(8), pages 1-11, August.
    11. Tao Liu & Zijian Ding & Jiayuan Yu & Wenwen Zhang, 2023. "Parameter Estimation for Nonlinear Diffusion Problems by the Constrained Homotopy Method," Mathematics, MDPI, vol. 11(12), pages 1-12, June.
    12. Tao Liu & Jiayuan Yu & Yuanjin Zheng & Chao Liu & Yanxiong Yang & Yunfei Qi, 2022. "A Nonlinear Multigrid Method for the Parameter Identification Problem of Partial Differential Equations with Constraints," Mathematics, MDPI, vol. 10(16), pages 1-12, August.
    13. Li, Yibao & Xia, Qing & Kang, Seungyoon & Kwak, Soobin & Kim, Junseok, 2024. "A practical algorithm for the design of multiple-sized porous scaffolds with triply periodic structures," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 481-495.
    14. Jia Deng & Xiaolan Liu & Yan Sun & Mi Zhou, 2022. "Fixed Point Results for a New Rational Contraction in Double Controlled Metric-like Spaces," Mathematics, MDPI, vol. 10(9), pages 1-12, April.
    15. Umar Ishtiaq & Doha A. Kattan & Khaleel Ahmad & Salvatore Sessa & Farhan Ali, 2023. "Fixed Point Results in Controlled Fuzzy Metric Spaces with an Application to the Transformation of Solar Energy to Electric Power," Mathematics, MDPI, vol. 11(15), pages 1-17, August.
    16. Gunaseelan Mani & Salma Haque & Arul Joseph Gnanaprakasam & Ozgur Ege & Nabil Mlaiki, 2023. "The Study of Bicomplex-Valued Controlled Metric Spaces with Applications to Fractional Differential Equations," Mathematics, MDPI, vol. 11(12), pages 1-19, June.
    17. Irshad Ayoob & Ng Zhen Chuan & Nabil Mlaiki, 2023. "Double-Composed Metric Spaces," Mathematics, MDPI, vol. 11(8), pages 1-12, April.

    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:1390-:d:1096033. 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.