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Common fixed points of strict contractions in Menger spaces

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Abstract

The aim of this paper is to prove some common fixed point theorems under certain strict contractive conditions for mappings sharing the common property (E.A) in Menger spaces. As applications to our results, we obtain the corresponding common fixed point theorems under strict contraction in metric spaces. Thus, our results generalize many known results in Menger as well as metric spaces. Some related results are also derived besides presenting several illustrative examples.

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References

  1. A. Aamri and D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl., 270 (2002), 181–188.

    Article  MathSciNet  MATH  Google Scholar 

  2. M. S. El Naschie, A review of applications and results of E-infinity theory, Int. J. Nonlinear Sci. Numer. Simul., 8 (2007), 11–20.

    Article  Google Scholar 

  3. J.-X. Fang and Y. Gao, Common fixed point theorems under strict contractive conditions in Menger spaces, Nonlinear Anal., 70 (2009), 184–193.

    Article  MathSciNet  MATH  Google Scholar 

  4. O. Hadzić and E. Pap, Fixed Point Theory in Probabilistic Metric Spaces, Kluwer Academic Publishers (Dordrecht, 2001).

    Google Scholar 

  5. M. Imdad, Javid Ali and L. Khan, Coincidence and fixed points in symmetric spaces under strict contractions, J. Math. Anal. Appl., 320 (2006), 352–360.

    Article  MathSciNet  MATH  Google Scholar 

  6. M. Imdad and Javid Ali, Jungck’s common fixed point theorem and E.A property, Acta Math. Sinica, 24 (2008), 87–94.

    Article  MathSciNet  MATH  Google Scholar 

  7. M. Imdad, Javid Ali and M. Tanveer, Coincidence and common fixed point theorems for nonlinear contractions in Menger PM spaces, Chaos, Solitons & Fractals, 42 (2009), 3121–3129.

    Article  MathSciNet  MATH  Google Scholar 

  8. G. Jungck, Compatible mappings and common fixed points, Internat. J. Math. Math. Sci., 9 (1986), 771–779.

    Article  MathSciNet  MATH  Google Scholar 

  9. G. Jungck, Common fixed point for commuting and compatible maps on compacta, Proc. Amer. Math. Soc., 103 (1988), 977–983.

    Article  MathSciNet  MATH  Google Scholar 

  10. G. Jungck, Common fixed points for non continuous non self maps on non metric spaces, Far East J. Math. Sci., 4 (1996), 199–215.

    MathSciNet  MATH  Google Scholar 

  11. S. Kasahara and B. E. Rhoades, Common fixed point theorems in compact metric spaces, Math. Japon., 23 (1978), 227–229.

    MathSciNet  MATH  Google Scholar 

  12. I. Kubiaczyk and S. Sharma, Some common fixed point theorems in Menger space under strict contractive conditions, Southeast Asian Bull. Math., 32 (2008), 117–124.

    MathSciNet  MATH  Google Scholar 

  13. Y. Liu, Jun Wu and Z. Li, Common fixed points of single-valued and multi-valued maps, Internat. J. Math. Math. Sci., 19 (2005), 3045–3055.

    Article  MathSciNet  Google Scholar 

  14. K. Menger, Statistical metrics, Proc. Nat. Acad. Sci. USA, 28 (1942), 535–537.

    Article  MathSciNet  MATH  Google Scholar 

  15. K. Menger, Probabilistic geometry, Proc. Nat. Acad. Sci. USA, 37 (1951), 226–229.

    Article  MathSciNet  MATH  Google Scholar 

  16. D. Mihet, A note on a common fixed point theorem in probabilistic metric spaces, Acta Math. Hungar., 125 (2009), 127–130.

    Article  MathSciNet  MATH  Google Scholar 

  17. D. Mihet, Fixed point theorems in fuzzy metric spaces using property E.A, Nonlinear Anal., 73 (2010), 2184–2188.

    Article  MathSciNet  MATH  Google Scholar 

  18. D. Mihet, A generalization of a contraction principle in probabilistic metric spaces, II, Internat. J. Math. Math. Sci., 5 (2005), 729–736.

    Article  MathSciNet  Google Scholar 

  19. S. N. Mishra, Common fixed points of compatible mappings in PM-spaces, Math. Japon., 36 (1991), 283–289.

    MathSciNet  MATH  Google Scholar 

  20. R. P. Pant, Common fixed points of non commuting mappings, J. Math. Anal. Appl., 188 (1994), 436–440.

    Article  MathSciNet  MATH  Google Scholar 

  21. R. P. Pant, Common fixed points of contractive maps, J. Math. Anal. Appl., 226 (1998), 251–258.

    Article  MathSciNet  MATH  Google Scholar 

  22. R. P. Pant, R-weak commutativity and common fixed points, Soochow J. Math., 25 (1999), 37–42.

    MathSciNet  MATH  Google Scholar 

  23. R. P. Pant and V. Pant, Common fixed point under strict contractive conditions, J. Math. Anal. Appl., 248 (2000), 327–332.

    Article  MathSciNet  MATH  Google Scholar 

  24. A. Razani and M. Shirdaryazdi, A common fixed point theorem of compatible maps in Menger space, Chaos, Solitons & Fractals, 32 (2007), 26–34.

    Article  MathSciNet  MATH  Google Scholar 

  25. B. Schweizer and A. Sklar, Probabilistic Metric Spaces, Elsevier, North Holland (New York, 1983).

    MATH  Google Scholar 

  26. V. M. Sehgal and A. T. Bharucha-Reid, Fixed point of contraction mappings on probabilistic metric spaces, Math. Systems Theory, 6 (1972), 97–102.

    Article  MathSciNet  MATH  Google Scholar 

  27. B. Singh and S. Jain, A fixed point theorem in Menger space through weak compatibility, J. Math. Anal. Appl., 301 (2005), 439–448.

    Article  MathSciNet  MATH  Google Scholar 

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Ali, J., Imdad, M., Mihet, D. et al. Common fixed points of strict contractions in Menger spaces. Acta Math Hung 132, 367–386 (2011). https://doi.org/10.1007/s10474-011-0105-3

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  • DOI: https://doi.org/10.1007/s10474-011-0105-3

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