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Fixed points in intuitionistic fuzzy metric spaces

Author

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  • Alaca, Cihangir
  • Turkoglu, Duran
  • Yildiz, Cemil

Abstract

The purpose of this paper, using the idea of intuitionistic fuzzy set due to Atanassov [Atanassov K. Intuitionistic fuzzy sets. Fuzzy Sets Syst 1986;20:87–96], we define the notion of intuitionistic fuzzy metric spaces due to Kramosil and Michalek [Kramosil O, Michalek J. Fuzzy metric and statistical metric spaces. Kybernetika 1975;11:326–34]. Further the well-known fixed point theorems of Banach and Edelstein are extended to intuitionistic fuzzy metric spaces with the help of Grabiec [Grabiec M. Fixed points in fuzzy metric spaces. Fuzzy Sets Syst 1988;27:385–9].

Suggested Citation

  • Alaca, Cihangir & Turkoglu, Duran & Yildiz, Cemil, 2006. "Fixed points in intuitionistic fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 29(5), pages 1073-1078.
    • Handle: RePEc:eee:chsofr:v:29:y:2006:i:5:p:1073-1078
    DOI: 10.1016/j.chaos.2005.08.066
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    Cited by:

    1. 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.
    2. 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.
    3. Ješić, Siniša N. & Babačev, Nataša A., 2008. "Common fixed point theorems in intuitionistic fuzzy metric spaces and L-fuzzy metric spaces with nonlinear contractive condition," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 675-687.
    4. Qiu, Dong & Shu, Lan & Guan, Jian, 2009. "Common fixed point theorems for fuzzy mappings under Φ-contraction condition," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 360-367.
    5. 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.
    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. Saleem, Naeem & Ahmad, Khaleel & Ishtiaq, Umar & De la Sen, Manuel, 2023. "Multivalued neutrosophic fractals and Hutchinson-Barnsley operator in neutrosophic metric space," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    8. 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.
    9. Şuara Onbaşıoğlu & Banu Pazar Varol, 2023. "Intuitionistic Fuzzy Metric-like Spaces and Fixed-Point Results," Mathematics, MDPI, vol. 11(8), pages 1-15, April.
    10. 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.
    11. 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.
    12. 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.
    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. 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.

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