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Unified Fixed Point Theorems via Common Limit Range Property in Modified Intuitionistic Fuzzy Metric Spaces

Author

Listed:
  • Mohammad Imdad
  • Sunny Chauhan
  • Sumitra Dalal

Abstract

The purpose of this paper is to emphasize the role of “common limit range property” to ascertain the existence of common fixed points in modified intuitionistic fuzzy metric spaces enjoying an implicit function utilized in Tanveer et al. (2012) and Imdad et al. (2012). As an application to our main result, we derive a fixed point theorem for finite families of self‐mappings. We also give some examples which demonstrate the validity of the hypotheses and degree of generality of our main results. Our results improve and extend several previously known fixed point theorems of the existing literature.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:413473
    DOI: 10.1155/2013/413473
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    References listed on IDEAS

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    1. 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).
    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. Mohammad Imdad & Sunny Chauhan, 2013. "Employing Common Limit Range Property to Prove Unified Metrical Common Fixed Point Theorems," International Journal of Analysis, Hindawi, vol. 2013, pages 1-10, May.
    4. 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, Hindawi, vol. 2012, pages 1-13, August.
    5. 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.
    6. Alaca, Cihangir & Turkoglu, Duran & Yildiz, Cemil, 2006. "Fixed points in intuitionistic fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 29(5), pages 1073-1078.
    7. Sunny Chauhan & M. Alamgir Khan & Wutiphol Sintunavarat, 2013. "Common Fixed Point Theorems in Fuzzy Metric Spaces Satisfying -Contractive Condition with Common Limit Range Property," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-14, September.
    8. 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.
    9. Nguyen Manh Hung & Erdal Karapınar & Nguyen Van Luong, 2012. "Coupled Coincidence Point Theorem in Partially Ordered Metric Spaces via Implicit Relation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    10. 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).
    11. 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.
    12. 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).
    13. Gerald Jungck, 1986. "Compatible mappings and common fixed points," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 9, pages 1-9, January.
    14. Nguyen Manh Hung & Erdal Karapınar & Nguyen Van Luong, 2012. "Coupled Coincidence Point Theorem in Partially Ordered Metric Spaces via Implicit Relation," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-14, July.
    15. 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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