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Common Fixed Point Theorems in Fuzzy Metric Spaces Satisfying ϕ‐Contractive Condition with Common Limit Range Property

Author

Listed:
  • Sunny Chauhan
  • M. Alamgir Khan
  • Wutiphol Sintunavarat

Abstract

The objective of this paper is to emphasize the role of “common limit range property” to ascertain the existence of common fixed point in fuzzy metric spaces. Some illustrative examples are furnished which demonstrate the validity of the hypotheses and degree of utility of our results. We derive a fixed point theorem for four finite families of self‐mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. As an application to our main result, we prove an integral‐type fixed point theorem in fuzzy metric space. Our results improve and extend a host of previously known results including the ones contained in Imdad et al. (2012).

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:735217
    DOI: 10.1155/2013/735217
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    References listed on IDEAS

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    1. A. Branciari, 2002. "A fixed point theorem for mappings satisfying a general contractive condition of integral type," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 29, pages 1-6, January.
    2. Ismat Beg & Shaban Sedghi & Nabi Shobe, 2013. "Fixed Point Theorems in Fuzzy Metric Spaces," International Journal of Analysis, Hindawi, vol. 2013, pages 1-4, January.
    3. Imdad, M. & Ali, Javid & Tanveer, M., 2009. "Coincidence and common fixed point theorems for nonlinear contractions in Menger PM spaces," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3121-3129.
    4. Yicheng Liu & Jun Wu & Zhixiang Li, 2005. "Common fixed points of single-valued and multivalued maps," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-11, January.
    5. 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.
    6. 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).
    7. 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.
    8. Bijendra Singh & Shishir Jain, 2005. "Semicompatibility and fixed point theorems in fuzzy metric space using implicit relation," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-13, January.
    9. Wutiphol Sintunavarat & Poom Kumam, 2011. "Common Fixed Point Theorems for a Pair of Weakly Compatible Mappings in Fuzzy Metric Spaces," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-14, August.
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    Cited by:

    1. Ayush Bartwal & Junaid Ahmad & R. C. Dimri & Gopi Prasad & Ebenezer Bonyah, 2022. "On Some New Common Fixed Point Results for Finite Number of Mappings in Fuzzy Metric Spaces," Advances in Mathematical Physics, John Wiley & Sons, vol. 2022(1).
    2. 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).
    3. 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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