IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i2p270-d1025364.html
   My bibliography  Save this article

Fixed Point Approach: Ulam Stability Results of Functional Equation in Non-Archimedean Fuzzy φ -2-Normed Spaces and Non-Archimedean Banach Spaces

Author

Listed:
  • Kandhasamy Tamilvanan

    (Department of Mathematics, Faculty of Science & Humanities, R.M.K. Engineering College, Srivilliputhur 601 206, Tamil Nadu, India)

  • Ali H. Alkhaldi

    (Department of Mathematics, College of Science, King Khalid University, Abha 61421, Saudi Arabia)

  • Ravi P. Agarwal

    (Department of Mathematics, Texas A & M University-Kingsville, 700 University Blvd., Kingsville, TX 78363-8202, USA)

  • Abdulaziz M. Alanazi

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

Abstract

In this work, we introduce a new type of generalized mixed-type quadratic-additive functional equation and obtain its general solution. The main goal of this work is to investigate Ulam stability of this mixed type of quadratic-additive functional equation in the setting of non-Archimedean fuzzy φ -2-normed space and non-Archimedean Banach space using the direct and fixed point approaches by taking into our account two cases: even mapping and odd mapping.

Suggested Citation

  • Kandhasamy Tamilvanan & Ali H. Alkhaldi & Ravi P. Agarwal & Abdulaziz M. Alanazi, 2023. "Fixed Point Approach: Ulam Stability Results of Functional Equation in Non-Archimedean Fuzzy φ -2-Normed Spaces and Non-Archimedean Banach Spaces," Mathematics, MDPI, vol. 11(2), pages 1-24, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:270-:d:1025364
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/2/270/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/2/270/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Saadati, Reza & Park, Jin Han, 2006. "On the intuitionistic fuzzy topological spaces," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 331-344.
    2. Soon-Mo Jung & Dorian Popa & Michael Rassias, 2014. "On the stability of the linear functional equation in a single variable on complete metric groups," Journal of Global Optimization, Springer, vol. 59(1), pages 165-171, May.
    3. Mohiuddine, S.A. & Danish Lohani, Q.M., 2009. "On generalized statistical convergence in intuitionistic fuzzy normed space," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1731-1737.
    4. Zbigniew Gajda, 1991. "On stability of additive mappings," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 14, pages 1-4, 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. Elhoucien Elqorachi & Michael Th. Rassias, 2018. "Generalized Hyers-Ulam Stability of Trigonometric Functional Equations," Mathematics, MDPI, vol. 6(5), pages 1-11, May.
    2. Mohiuddine, S.A., 2009. "Stability of Jensen functional equation in intuitionistic fuzzy normed space," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2989-2996.
    3. Jae-Hyeong Bae & Ick-Soon Chang & Hark-Mahn Kim, 2022. "Almost Generalized Derivation on Banach Algebras," Mathematics, MDPI, vol. 10(24), pages 1-8, December.
    4. Mursaleen, M. & Mohiuddine, S.A., 2009. "Nonlinear operators between intuitionistic fuzzy normed spaces and Fréchet derivative," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1010-1015.
    5. Ick-Soon Chang & Yang-Hi Lee & Jaiok Roh, 2023. "Representation and Stability of General Nonic Functional Equation," Mathematics, MDPI, vol. 11(14), pages 1-19, July.
    6. Mursaleen, M. & Mohiuddine, S.A., 2009. "On stability of a cubic functional equation in intuitionistic fuzzy normed spaces," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2997-3005.
    7. Saadati, Reza, 2008. "Notes to the paper “Fixed points in intuitionistic fuzzy metric spaces” and its generalization to L-fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 176-180.
    8. Ponmana Selvan Arumugam & Won-Gil Park & Jaiok Roh, 2024. "Stability and Instability of an Apollonius-Type Functional Equation," Mathematics, MDPI, vol. 12(14), pages 1-11, July.
    9. Mursaleen, M. & Danish Lohani, Q.M., 2009. "Intuitionistic fuzzy 2-normed space and some related concepts," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 224-234.
    10. 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.
    11. Fang Wang & Ying Gao, 2022. "The Analysis of Hyers–Ulam Stability for Heat Equations with Time-Dependent Coefficient," Mathematics, MDPI, vol. 10(22), pages 1-10, November.
    12. Bivas Dinda & Santanu Kumar Ghosh & T. K. Samanta, 2019. "Intuitionistic Fuzzy Pseudo-Normed Linear Spaces," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 113-127, March.
    13. Saadati, R. & Sedghi, S. & Shobe, N., 2008. "Modified intuitionistic fuzzy metric spaces and some fixed point theorems," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 36-47.
    14. Goudarzi, M. & Vaezpour, S.M. & Saadati, R., 2009. "On the intuitionistic fuzzy inner product spaces," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1105-1112.
    15. P. Agilan & K. Julietraja & Mohammed M. A. Almazah & Ammar Alsinai, 2023. "Stability Analysis of a New Class of Series Type Additive Functional Equation in Banach Spaces: Direct and Fixed Point Techniques," Mathematics, MDPI, vol. 11(4), pages 1-19, February.
    16. Kandhasamy Tamilvanan & Yahya Almalki & Syed Abdul Mohiuddine & Ravi P. Agarwal, 2022. "Stability Results of Quadratic-Additive Functional Equation Based on Hyers Technique in Matrix Paranormed Spaces," Mathematics, MDPI, vol. 10(11), pages 1-17, June.
    17. Heejeong Koh, 2023. "Stability Estimates for an Arithmetic Functional Equation with Brzdȩk Fixed Point Approaches," Mathematics, MDPI, vol. 11(7), pages 1-10, March.
    18. Razani, Abdolrahman, 2006. "Existence of fixed point for the nonexpansive mapping of intuitionistic fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 30(2), pages 367-373.
    19. Abdulaziz M. Alanazi & G. Muhiuddin & K. Tamilvanan & Ebtehaj N. Alenze & Abdelhalim Ebaid & K. Loganathan, 2020. "Fuzzy Stability Results of Finite Variable Additive Functional Equation: Direct and Fixed Point Methods," Mathematics, MDPI, vol. 8(7), pages 1-14, June.
    20. Nabanita Konwar & Ayhan Esi & Pradip Debnath, 2019. "New Fixed Point Theorems via Contraction Mappings in Complete Intuitionistic Fuzzy Normed Linear Space," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 65-83, March.

    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:2:p:270-:d:1025364. 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.