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A coincidence point result in Menger spaces using a control function

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  • Choudhury, Binayak S.
  • Das, Krishnapada

Abstract

In the present work we prove a coincidence point theorem in Menger spaces with a t-norm T which satisfies the condition sup{T(t,t):t<1}=1. As a corollary of our theorem we obtain some existing results in metric spaces and probabilistic metric spaces. Particularly our result implies a probabilistic generalization of Banach contraction mapping theorem. We also support our result by an example.

Suggested Citation

  • Choudhury, Binayak S. & Das, Krishnapada, 2009. "A coincidence point result in Menger spaces using a control function," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3058-3063.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:5:p:3058-3063
    DOI: 10.1016/j.chaos.2009.04.020
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    References listed on IDEAS

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    1. Miheţ, Dorel, 2009. "Fixed point theorems in probabilistic metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 1014-1019.
    2. Razani, Abdolrahman & Shirdaryazdi, Maryam, 2007. "A common fixed point theorem of compatible maps in Menger space," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 26-34.
    3. Rezaiyan, R. & Cho, Y.J. & Saadati, R., 2008. "A common fixed point theorem in Menger probabilistic quasi-metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1153-1157.
    4. Alimohammady, Mohsen & Esmaeli, Abdolreza & Saadati, Reza, 2009. "Completeness results in probabilistic metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 765-769.
    5. Miheţ, Dorel, 2009. "A note on a fixed point theorem in Menger probabilistic quasi-metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2349-2352.
    6. Razani, Abdolrahman & Fouladgar, Kaveh, 2007. "Extension of contractive maps in the Menger probabilistic metric space," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1724-1731.
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    Cited by:

    1. Gopal, Dhananjay & Abbas, Mujahid & Vetro, Calogero, 2014. "Some new fixed point theorems in Menger PM-spaces with application to Volterra type integral equation," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 955-967.

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