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Unified Common Fixed Point Theorems for a Hybrid Pair of Mappings via an Implicit Relation Involving Altering Distance Function

Author

Listed:
  • Sunny Chauhan
  • Muhammad Alamgir Khan
  • Zoran Kadelburg
  • Mohammad Imdad

Abstract

The object of this paper is to emphasize the role of a suitable implicit relation involving altering distance function which covers a multitude of contraction conditions in one go. By using this implicit relation, we prove a new coincidence and common fixed point theorem for a hybrid pair of occasionally coincidentally idempotent mappings in a metric space employing the common limit range property. Our main result improves and generalizes a host of previously known results. We also utilize suitable illustrative examples to substantiate the realized improvements in our results.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:718040
    DOI: 10.1155/2014/718040
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    References listed on IDEAS

    as
    1. Hideaki Kaneko & Salvatore Sessa, 1989. "Fixed point theorems for compatible multi-valued and single-valued mappings," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 12, pages 1-6, January.
    2. 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.
    3. Shyam Lal Singh & Ki Sik Ha & Yeol Je Cho, 1989. "Coincidence and fixed points of nonlinear Hybrid contractions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 12, pages 1-10, January.
    4. Zoran Kadelburg & Stojan Radenović & Naseer Shahzad, 2013. "A Note on Various Classes of Compatible-Type Pairs of Mappings and Common Fixed Point Theorems," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-6, November.
    5. Zoran Kadelburg & Stojan Radenović & Naseer Shahzad, 2013. "A Note on Various Classes of Compatible‐Type Pairs of Mappings and Common Fixed Point Theorems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    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. 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. Lucas Wangwe, 2022. "Coincidence Fixed‐Point Theorems for p‐Hybrid Contraction Mappings in Gb‐Metric Space with Application," Abstract and Applied Analysis, John Wiley & Sons, vol. 2022(1).

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