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Common Fixed Point Theorems for a Pair of Weakly Compatible Mappings in Fuzzy Metric Spaces

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  • Wutiphol Sintunavarat
  • Poom Kumam

Abstract

We prove some common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces both in the sense of Kramosil and Michalek and in the sense of George and Veeramani by using the new property and give some examples. Our results improve and generalize the main results of Mihet in (Mihet, 2010) and many fixed point theorems in fuzzy metric spaces.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnljam:v:2011:y:2011:i:1:n:637958
    DOI: 10.1155/2011/637958
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    References listed on IDEAS

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    1. 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.
    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. W. Sintunavarat & P. Kumam, 2011. "Gregus-Type Common Fixed Point Theorems for Tangential Multivalued Mappings of Integral Type in Metric Spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2011, pages 1-12, April.
    4. B. E. Rhoades, 1995. "A common fixed point theorem for a sequence of fuzzy mappings," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 18, pages 1-3, January.
    5. V. H. Badshah & Varsha Joshi, 2011. "Semicompatibility and Fixed Point Theorems for Reciprocally Continuous Maps in a Fuzzy Metric Space," Journal of Applied Mathematics, John Wiley & Sons, vol. 2011(1).
    6. 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.
    7. Chirasak Mongkolkeha & Poom Kumam, 2011. "Fixed Point and Common Fixed Point Theorems for Generalized Weak Contraction Mappings of Integral Type in Modular Spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2011, pages 1-12, June.
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    Cited by:

    1. Marwan Amin Kutbi & Mohammad Imdad & Sunny Chauhan & Wutiphol Sintunavarat, 2014. "Some Integral Type Fixed Point Theorems for Non‐Self‐Mappings Satisfying Generalized (ψ, φ)‐Weak Contractive Conditions in Symmetric Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Sunny Chauhan & Muhammad Alamgir Khan & Zoran Kadelburg & Mohammad Imdad, 2014. "Unified Common Fixed Point Theorems for a Hybrid Pair of Mappings via an Implicit Relation Involving Altering Distance Function," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    3. Manish Jain & Kenan Tas & Sanjay Kumar & Neetu Gupta, 2012. "Coupled Fixed Point Theorems for a Pair of Weakly Compatible Maps along with CLRg Property in Fuzzy Metric Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    4. Sunny Chauhan & M. Alamgir Khan & Wutiphol Sintunavarat, 2013. "Common Fixed Point Theorems in Fuzzy Metric Spaces Satisfying ϕ‐Contractive Condition with Common Limit Range Property," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    5. Mohammad Imdad & Sunny Chauhan & Sumitra Dalal, 2013. "Unified Fixed Point Theorems via Common Limit Range Property in Modified Intuitionistic Fuzzy Metric Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    6. Mahpeyker Öztürk, 2014. "Common Fixed Point Theorems Satisfying Contractive Type Conditions in Complex Valued Metric Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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