IDEAS home Printed from https://ideas.repec.org/a/wsi/nmncxx/v15y2019i01ns1793005719500042.html
   My bibliography  Save this article

New Fixed Point Theorems via Contraction Mappings in Complete Intuitionistic Fuzzy Normed Linear Space

Author

Listed:
  • Nabanita Konwar

    (Department of Mathematics, North Eastern Regional Institute of Science and Technology, Nirjuli, Arunachal Pradesh 791109, India)

  • Ayhan Esi

    (#x2020;Department of Mathematics, Science and Art Faculty, Adiyaman University, TR-02040 Adiyaman, Turkey)

  • Pradip Debnath

    (#x2021;Department of Applied Science and Humanities, Assam University, Silchar, Cachar, Silchar 788011, India)

Abstract

Contraction mappings provide us with one of the major sources of fixed point theorems. In many mathematical models, the existence of a solution may often be described by the existence of a fixed point for a suitable map. Therefore, study of such mappings and fixed point results becomes well motivated in the setting of intuitionistic fuzzy normed linear spaces (IFNLSs) as well. In this paper, we define some new contraction mappings and establish fixed point theorems in a complete IFNLS. Our results unify and generalize several classical results existing in the literature.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:nmncxx:v:15:y:2019:i:01:n:s1793005719500042
    DOI: 10.1142/S1793005719500042
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S1793005719500042
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S1793005719500042?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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. Alaca, Cihangir & Turkoglu, Duran & Yildiz, Cemil, 2006. "Fixed points in intuitionistic fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 29(5), pages 1073-1078.
    3. AL. Narayanan & S. Vijayabalaji, 2005. "Fuzzy n -normed linear space," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-15, January.
    4. V. H. Badshah & Varsha Joshi, 2011. "Semicompatibility and Fixed Point Theorems for Reciprocally Continuous Maps in a Fuzzy Metric Space," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-12, April.
    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. 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.
    2. 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.
    3. Karakus, S. & Demirci, K. & Duman, O., 2008. "Statistical convergence on intuitionistic fuzzy normed spaces," Chaos, Solitons & Fractals, Elsevier, vol. 35(4), pages 763-769.
    4. Mursaleen, M. & Mohiuddine, S.A., 2009. "Statistical convergence of double sequences in intuitionistic fuzzy normed spaces," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2414-2421.
    5. 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.
    6. Ćirić, Ljubomir B. & Ješić, Siniša N. & Ume, Jeong Sheok, 2008. "The existence theorems for fixed and periodic points of nonexpansive mappings in intuitionistic fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 781-791.
    7. 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.
    8. 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.
    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. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Mathuraiveeran Jeyaraman & Mookiah Suganthi & Wasfi Shatanawi, 2020. "Common Fixed Point Theorems in Intuitionistic Generalized Fuzzy Cone Metric Spaces," Mathematics, MDPI, vol. 8(8), pages 1-13, July.
    15. 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.
    16. 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.
    17. P. Saha & T. K. Samanta & Pratap Mondal & B. S. Choudhury & Manuel De La Sen, 2020. "Applying Fixed Point Techniques to Stability Problems in Intuitionistic Fuzzy Banach Spaces," Mathematics, MDPI, vol. 8(6), pages 1-15, June.
    18. Mohiuddine, S.A., 2009. "Stability of Jensen functional equation in intuitionistic fuzzy normed space," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2989-2996.
    19. Saadati, Reza, 2009. "A note on “Some results on the IF-normed spaces”," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 206-213.
    20. R. Saadati, 2011. "Some results on the ℒ-fuzzy topological isomorphism," Fuzzy Information and Engineering, Springer, vol. 3(4), pages 385-391, December.

    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:wsi:nmncxx:v:15:y:2019:i:01:n:s1793005719500042. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/nmnc/nmnc.shtml .

    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.