DOI QR코드

DOI QR Code

Fixed Point Theorems for Weakly Compatible Functions using (JCLR) Property in Intuitionistic Fuzzy Metric Space

  • Park, Jong Seo (Department of Mathematic Education, Chinju National University of Education)
  • Received : 2012.11.30
  • Accepted : 2012.12.24
  • Published : 2012.12.25

Abstract

In this paper, we give definitions for common limit in the range property of mappings and obtain common fixed point theorem for a pair of weakly compatible functions in intuitionistic fuzzy metric space using the joint common limit in the range property of mappings(shortly, (JCLR) property). Our results improve and generalize results of Chauhan et al[1].

Keywords

References

  1. S. Chauhan, W. Sintunavarat, P. Kumam, "Common fixed point theorems for weakly compatible mappings in fuzzy metric spaces using (JCLR) property," Applied Math., vol. 3, pp.976-982, 2012. https://doi.org/10.4236/am.2012.39145
  2. A. George, P. Veeramani, "On some results of analysis for fuzzy metric spaces," Fuzzy Sets and Systems, vol. 90, pp. 365-368, 1997. https://doi.org/10.1016/S0165-0114(96)00207-2
  3. M. Imdad, J. Ali, "Some common fixed point theorems in fuzzy metric spaces," Math. Commun., vol. 11, pp. 153-163, 2006.
  4. J. Kramosil, J. Michalek, "Fuzzy metric and statistical metric spaces," Kybernetica, vol. 11, pp. 326-334, 1975.
  5. J.S. Park, "On fixed point theorem of weak compatible maps of type($\gamma$) in complete intuitionistic fuzzy metric space," Int. J. F. I. S., vol. 11, no. 1, pp. 38-43, 2011.
  6. J.S. Park, "Some fixed point theorem using common property(E.A.) in intuitionistic fuzzy metric space," J. Korean Soc. Math. Educ. Ser. B, vol. 18, no. 3, pp. 255-260, 2011. https://doi.org/10.7468/jksmeb.2011.18.3.255
  7. J.S. Park, " Fixed point theorem for common property( E.A.) and weak compatible functions in intuitionistic fuzzy metric space," KIIS., vol. 11, no. 3, pp. 149-152, 2011. https://doi.org/10.5391/IJFIS.2011.11.3.149
  8. J.S. Park, J.H. Park, Y.C. Kwun, "On some results for five mappings using compatibility of type( ) in intuitionistic fuzzy metric space," International J. Fuzzy Logic Intelligent Systems, vol. 8, no. 4, pp. 299-305, 2008. https://doi.org/10.5391/IJFIS.2008.8.4.299
  9. B. Singh, S. Jain, "Weak compatibility and fixed point theorems in fuzzy metric space," Ganita, vol. 56, pp. 167-176, 2005.
  10. L.A. Zadeh, "Fuzzy sets," Inform. and Control, vol. 8, pp. 338-353, 1965. https://doi.org/10.1016/S0019-9958(65)90241-X

Cited by

  1. Some Common Fixed Points for Type(β) Compatible Maps in an Intuitionistic Fuzzy Metric Space vol.13, pp.2, 2013, https://doi.org/10.5391/IJFIS.2013.13.2.147
  2. Common Fixed Point and Example for Type(β) Compatible Mappings with Implicit Relation in an Intuitionistic Fuzzy Metric Space vol.14, pp.1, 2014, https://doi.org/10.5391/IJFIS.2014.14.1.66
  3. On Common Fixed Point for Single and Set-Valued Maps Satisfying OWC Property in IFMS using Implicit Relation vol.15, pp.2, 2015, https://doi.org/10.5391/IJFIS.2015.15.2.132