Pure and Applied Mathematics Journal

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Common Fixed Point Theorem in Fuzzy Metric Spaces Under E. A. Like Property

Received: 04 July 2016    Accepted: 25 July 2016    Published: 21 August 2016
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Abstract

George and Veeramani [1] modify the concept of fuzzy metric spaces introduced by Kramosil and Michalek [4], Aamri and Moutawakil [8] generalized the notion of non-compatible mapping in metric space by E.A. property.Continuing the above conceptwe prove some commonfixed point theorem for a pair of weakly compatible maps under E.A. Like property.

DOI 10.11648/j.pamj.20160504.18
Published in Pure and Applied Mathematics Journal (Volume 5, Issue 4, August 2016)
Page(s) 141-144
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Fuzzy Metric Space, E. A. Property, E. A. Like Property, Weakly Compatible Maps

References
[1] A. George and P. Veeramani. On some results in fuzzy metric spaces. Fuzzy Sets and Systems, 64: 395: 399, 1994.
[2] B. Schweizer and ASklar. Probabilistic Metric Spaces. North Holland, 1983.
[3] G. Jungck and B. E. Rhoades. Fixed point for set valued functions without continuity. Indian J. Pure and Appl. Math., 29(3): 227: 238, 1998.
[4] I. Kramosil and J. Michalek. Fuzzy metric and statistical metric spaces. Kybernetika, 15: 326: 334, 1975.
[5] J. X. Fang and Y. Gao. Common _xed point theorems under strict contractive conditions in menger spaces. Nonlin. Anal. (TMA), 70(1): 184: 193, 2009.
[6] Kamal Wadhwa, HariomDubeyand Reena Jain,Impact of E. A. Like" Property on Common Fixed Point Theorems in Fuzzy Metric Spaces, Journal of Advanced Studies in Topology, Vol. 3, No. 1, 2012, 52-59.
[7] L. A. Zadeh. Fuzzy sets. Infor. Control, 18: 338: 353, 1965.
[8] M. Aamri and D. El Moutawakil. Some new common fixed point theorems under strict contractive conditions. J. Math. Anal.Appl., 27: 181: 188, 2002.
[9] M. Imdad and J. Ali. Some common fixed point theorems in fuzzy metric spaces. Math. Commun., 11: 153: 163, 2006.
[10] P. Vijayaruju and Z. M. I. Sajath. Some common fixed point theorems in fuzzy metric spaces. Inter. J. of Math. Anal., 3(15): 701: 710, 2009.
[11] R. P. Pant. Common fixed point for non-commuting mappings. J. Math. Anal. Appl., 188: 436: 440, 1994.
[12] R. Vasuki. Commonfixed points for R-weakly commuting maps in fuzzy metric spaces. Indian J. Pure Appl. Math., 30: 419: 423,1999.
[13] S. Kumar. Insert the title of the paper. J. Appl. Math. Inform., 29(1-2): 395: 405, 2011.
[14] S. Sessa. On a weak commutativity of mappings in fixed point considerations. Publ. Inst. Math., 32(46): 149: 153, 1982.
[15] V. Pant. Some fixed point theorems in fuzzy metric spaces. Tamkang J. of Math., 40: 59: 66, 2009.
Author Information
  • TIT Group of Instititution, Bhopal, India

  • Retd. Additional Director, Bhopal, India

  • Govt. M. V. M. College, Bhopal, India

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  • APA Style

    Madhu Shrivastava, K. Qureshi, A. D. Singh. (2016). Common Fixed Point Theorem in Fuzzy Metric Spaces Under E. A. Like Property. Pure and Applied Mathematics Journal, 5(4), 141-144. https://doi.org/10.11648/j.pamj.20160504.18

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    ACS Style

    Madhu Shrivastava; K. Qureshi; A. D. Singh. Common Fixed Point Theorem in Fuzzy Metric Spaces Under E. A. Like Property. Pure Appl. Math. J. 2016, 5(4), 141-144. doi: 10.11648/j.pamj.20160504.18

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    AMA Style

    Madhu Shrivastava, K. Qureshi, A. D. Singh. Common Fixed Point Theorem in Fuzzy Metric Spaces Under E. A. Like Property. Pure Appl Math J. 2016;5(4):141-144. doi: 10.11648/j.pamj.20160504.18

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  • @article{10.11648/j.pamj.20160504.18,
      author = {Madhu Shrivastava and K. Qureshi and A. D. Singh},
      title = {Common Fixed Point Theorem in Fuzzy Metric Spaces Under E. A. Like Property},
      journal = {Pure and Applied Mathematics Journal},
      volume = {5},
      number = {4},
      pages = {141-144},
      doi = {10.11648/j.pamj.20160504.18},
      url = {https://doi.org/10.11648/j.pamj.20160504.18},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.pamj.20160504.18},
      abstract = {George and Veeramani [1] modify the concept of fuzzy metric spaces introduced by Kramosil and Michalek [4], Aamri and Moutawakil [8] generalized the notion of non-compatible mapping in metric space by E.A. property.Continuing the above conceptwe prove some commonfixed point theorem for a pair of weakly compatible maps under E.A. Like property.},
     year = {2016}
    }
    

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