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Common Fixed Points by Using E.A. Property in Fuzzy Metric Spaces

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Proceedings of the Third International Conference on Soft Computing for Problem Solving

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 259))

Abstract

In last some decades, Fuzzy topology has been extensively used in logic programming. It has been noticed by several researchers that, this theory was applied on various logical program to find more truthful result. The strength of fuzzy mathematics lies in its usefulness and having fruitful applications especially outside mathematics. In this paper, we prove some common fixed point theorem by using E.A. property in fuzzy metric spaces. We prove our results in fuzzy metric spaces in the sense of Kramosil and Michalek [1]. Our result generalize and extend relevant result of Mihet [2] and Vijayaraju [3]. An application of finite families of self mappings is given to support our result.

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References

  1. Kramosil, I., Michalek, J.: Fuzzy metric and Statistical metric spaces. Ky-bernetica 11, 326–334 (1975)

    MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  3. Vijayaraju, P., Sajath, Z.M.I.: Some common fixed point theorems in fuzzy metric spaces. Int. J. Math. Anal. 3, 701–710 (2009)

    MATH  MathSciNet  Google Scholar 

  4. Zadeh, L.A.: Fuzzy sets. Inform. Control 8, 338–353 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  5. Gregori, V., Morillas, S., Sapena, A.: Examples of fuzzy metrics and applications. Fuzzy Sets Syst. 170, 95–111 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  6. George, A., Veeramani, P.: On some results in fuzzy metric spaces. Fuzzy Sets Syst. 64, 395–399 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  7. Schweizer, B., Sklar, A.: Statistical metric spaces. Pacific J. Math. 10, 313–334 (1960)

    Article  MATH  MathSciNet  Google Scholar 

  8. Grabiec, M.: Fixed point in fuzzy metric spaces. Fuzzy Sets Syst. 27, 385–389 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  9. Banach, S: Sur les operations dans les ensembles abstraits et leur application aux equations integrals. Fundamenta Mathematicae. 3, 133–181 (1922)

    Google Scholar 

  10. Subrahmanyan, P.V.: A common fixed point theorem in fuzzy metric space. Inform. Sci. 83, 109–112 (1995)

    Article  MathSciNet  Google Scholar 

  11. Vasuki, R.: A common fixed point theorem in fuzzy metric space. Fuzzy Sets Syst. 97, 395–397 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  12. Saini, R.K., Vishal, Gupta: Fuzzy version of some fixed points theorems on expansion type maps in fuzzy metric space. J. Math. Assoc. Thai. 5, 245–252 (2007)

    MATH  MathSciNet  Google Scholar 

  13. Saini, R.K., Vishal, Gupta: Common coincidence points of R-weakly commuting fuzzy maps. J. Math. Assoc. Thai. 6, 109–115 (2008)

    MATH  Google Scholar 

  14. Vishal, Gupta, Ashima, Kanwar: Fixed point theorem in fuzzy metric spaces satisfying E.A property. Indian J. Sci. Technol. 5, 69–71 (2012)

    Google Scholar 

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

    Article  Google Scholar 

  16. Imdad, M., Ali, J.: Some common fixed point theorems in fuzzy metric spaces. Math. Commun. 11, 153–163 (2006)

    MATH  MathSciNet  Google Scholar 

  17. El Naschie, M.S.: A review of E-infinity theory and the mass spectrum of high energy particle physics. Chaos, Solitons Fractals 19, 209–236 (2004)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Maharishi Markandeshwar University, Mullana, Ambala, 133207, Haryana, India

    Vishal Gupta & Naveen Mani

Authors
  1. Vishal Gupta
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  2. Naveen Mani
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Corresponding author

Correspondence to Vishal Gupta .

Editor information

Editors and Affiliations

  1. Department of Paper Technology, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    Millie Pant

  2. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    Kusum Deep

  3. Department of Mathematics and Computer Science, Liverpool Hope University, Liverpool, United Kingdom

    Atulya Nagar

  4. Department of Applied Mathematics, South Asian University, New Delhi, India

    Jagdish Chand Bansal

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Gupta, V., Mani, N. (2014). Common Fixed Points by Using E.A. Property in Fuzzy Metric Spaces. In: Pant, M., Deep, K., Nagar, A., Bansal, J. (eds) Proceedings of the Third International Conference on Soft Computing for Problem Solving. Advances in Intelligent Systems and Computing, vol 259. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1768-8_4

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  • DOI: https://doi.org/10.1007/978-81-322-1768-8_4

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  • Publisher Name: Springer, New Delhi

  • Print ISBN: 978-81-322-1767-1

  • Online ISBN: 978-81-322-1768-8

  • eBook Packages: EngineeringEngineering (R0)

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