IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v35y2008i1p176-180.html
   My bibliography  Save this article

Notes to the paper “Fixed points in intuitionistic fuzzy metric spaces” and its generalization to L-fuzzy metric spaces

Author

Listed:
  • Saadati, Reza

Abstract

Recently, Alaca et al. [Alaca et al., Chaos, Solitons & Fractals 2006;29:1073–9] proved some fixed point theorems in intuitionistic fuzzy metric spaces by a strong definition of Cauchy sequence (see [George and Veeramani, Fuzzy Sets Syst 1994;64:395–9] and [Veeramani and Vasuki, Fuzzy Sets Syst 2003;135:409–13]), also the intuitionistic fuzzy metric space has extra conditions (see [Gregori et al., Chaos, Solitons & Fractals, 2006;28:902–5]). In this paper, we consider generalized intuitionistic fuzzy metric spaces i.e., L-fuzzy metric spaces and prove the fuzzy version of Banach and Edelstein contraction theorems in these spaces for modified definition of Cauchy sequence.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:chsofr:v:35:y:2008:i:1:p:176-180
    DOI: 10.1016/j.chaos.2006.05.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077906004565
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2006.05.005?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. El Naschie, Mohamed Saladin, 2006. "The idealized quantum two-slit gedanken experiment revisited—Criticism and reinterpretation," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 843-849.
    2. Saadati, Reza & Park, Jin Han, 2006. "On the intuitionistic fuzzy topological spaces," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 331-344.
    3. Tanaka, Yosuke & Mizuno, Yuzi & Kado, Tatsuhiko, 2005. "Chaotic dynamics in the Friedmann equation," Chaos, Solitons & Fractals, Elsevier, vol. 24(2), pages 407-422.
    4. Alaca, Cihangir & Turkoglu, Duran & Yildiz, Cemil, 2006. "Fixed points in intuitionistic fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 29(5), pages 1073-1078.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Martínez-Moreno, J. & Roldán, A. & Roldán, C., 2009. "A note on the L-fuzzy Banach’s contraction principle," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2399-2400.
    3. Deschrijver, Glad & O’Regan, Donal & Saadati, Reza & Mansour Vaezpour, S., 2009. "L-Fuzzy Euclidean normed spaces and compactness," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 40-45.

    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, 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.
    2. Saadati, Reza & Razani, Abdolrahman & Adibi, H., 2007. "A common fixed point theorem in L-fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 358-363.
    3. Deschrijver, Glad & O’Regan, Donal & Saadati, Reza & Mansour Vaezpour, S., 2009. "L-Fuzzy Euclidean normed spaces and compactness," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 40-45.
    4. 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.
    5. Sedghi, Shaban & Shobe, Nabi & Žikić-Došenović, Tatjana, 2009. "A common fixed point theorem in two complete fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2590-2596.
    6. 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.
    7. 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.
    8. Saadati, Reza, 2008. "On the L-fuzzy topological spaces," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1419-1426.
    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. 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. 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.
    12. Saadati, Reza, 2009. "A note on “Some results on the IF-normed spaces”," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 206-213.
    13. Karakus, S. & Demirci, K. & Duman, O., 2008. "Statistical convergence on intuitionistic fuzzy normed spaces," Chaos, Solitons & Fractals, Elsevier, vol. 35(4), pages 763-769.
    14. 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.
    15. Sadeqi, I. & Solaty kia, F., 2009. "Some fixed point theorems in fuzzy reflexive Banach spaces," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2606-2612.
    16. Tatjana Došenović & Dušan Rakić & Nebojša Ralević & Biljana Carić, 2024. "Note on Intuitionistic Fuzzy Metric-like Spaces with Application in Image Processing," Mathematics, MDPI, vol. 12(15), pages 1-19, July.
    17. Rezaiyan, R. & Cho, Y.J. & Saadati, R., 2008. "A common fixed point theorem in Menger probabilistic quasi-metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1153-1157.
    18. Khastan, A. & Ivaz, K., 2009. "Numerical solution of fuzzy differential equations by Nyström method," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 859-868.
    19. 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.
    20. Shams, M. & Vaezpour, S.M., 2009. "Best approximation on probabilistic normed spaces," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1661-1667.

    More about this item

    Statistics

    Access and download statistics

    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:eee:chsofr:v:35:y:2008:i:1:p:176-180. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.