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Generalized fixed point theorems for compatible mappings with some types in fuzzy metric spaces

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  • Cho, Yeol Je
  • Sedghi, Shaban
  • Shobe, Nabi

Abstract

In this paper, we give some new definitions of compatible mappings of types (I) and (II) in fuzzy metric spaces and prove some common fixed point theorems for four mappings under the condition of compatible mappings of types (I) and (II) in complete fuzzy metric spaces. Our results extend, generalize and improve the corresponding results given by many authors.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:5:p:2233-2244
    DOI: 10.1016/j.chaos.2007.06.108
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    References listed on IDEAS

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    1. S. N. Mishra & Nilima Sharma & S. L. Singh, 1994. "Common fixed points of maps on fuzzy metric spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 17, pages 1-6, January.
    2. Bijendra Singh & Shishir Jain & Shobha Jain, 2005. "Semicompatibility and fixed point theorems in an unbounded D -metric space," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-13, January.
    3. 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.
    4. Gerald Jungck, 1986. "Compatible mappings and common fixed points," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 9, pages 1-9, January.
    5. Tanaka, Yosuke & Mizuno, Yuzi & Kado, Tatsuhiko, 2005. "Chaotic dynamics in the Friedmann equation," Chaos, Solitons & Fractals, Elsevier, vol. 24(2), pages 407-422.
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    Cited by:

    1. Hsien-Chung Wu, 2018. "Near Fixed Point Theorems in the Space of Fuzzy Numbers," Mathematics, MDPI, vol. 6(7), pages 1-27, June.
    2. Wutiphol Sintunavarat & Poom Kumam, 2011. "Common Fixed Point Theorems for a Pair of Weakly Compatible Mappings in Fuzzy Metric Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2011(1).

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