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Employing Common Limit Range Property to Prove Unified Metrical Common Fixed Point Theorems

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  • Mohammad Imdad
  • Sunny Chauhan

Abstract

The purpose of this paper is to emphasize the role of “common limit range property” to ascertain the existence of common fixed point in metric spaces satisfying an implicit function essentially due to the paper of Ali and Imdad (2008). As an application to our main result, 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. Our results improve and extend a host of previously known results including the ones contained in the paper of Ali and Imdad (2008). We also furnish some illustrative examples to support our main results.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:ijanal:763261
    DOI: 10.1155/2013/763261
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Gerald Jungck, 1986. "Compatible mappings and common fixed points," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 9, pages 1-9, January.
    4. M. Imdad & M. S. Khan & S. Sessa, 1988. "On some weak conditions of commutativity in common fixed point theorems," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 11, pages 1-8, January.
    5. 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. Sunny Chauhan & Zoran Kadelburg & Sumitra Dalal, 2013. "A Common Fixed Point Theorem in Metric Space under General Contractive Condition," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(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).

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