International Journal of Fuzzy Logic and Intelligent Systems

  • 제14권1호
  • /
  • Pages.66-72
  • /
  • 2014
  • /
  • 1598-2645(pISSN)
  • /
  • 2093-744X(eISSN)
한국지능시스템학회 (Korean Institute of Intelligent Systems)
권호 표지
DOI QR코드

DOI QR Code

Common Fixed Point and Example for Type(β) Compatible Mappings with Implicit Relation in an Intuitionistic Fuzzy Metric Space

  • Park, Jong Seo (Department of Mathematic Education, Chinju National University of Education)
  • 투고 : 2013.12.03
  • 심사 : 2014.02.13
  • 발행 : 2014.03.25
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, we establish common fixed point theorem for type(${\beta}$) compatible four mappings with implicit relations defined on an intuitionistic fuzzy metric space. Also, we present the example of common fixed point satisfying the conditions of main theorem in an intuitionistic fuzzy metric space.

키워드

참고문헌

  1. L.A. Zadeh, "Fuzzy sets," Information and control, vol. 8, pp. 338-353, Jun. 1965. http://dx.doi.org/10.1016/S0019-9958(65)90241-X
  2. M. Grabiec, "Fixed point in fuzzy metric spaces," Fuzzy Sets and Systems, vol. 27, no. 3, pp. 385-389, Sep. 1988. http://dx.doi.org/10.1016/0165-0114(88)90064-4
  3. I. Altun, D. and Turkoglu, "Some fixed point theorems on fuzzy metric spaces with implicit relations," Communications of the Korean Mathematical Society, vol. 23, no. 1, pp. 111-124, Jan. 2008. .http://dx.doi.org/10.4134/CKMS.2008.23.1.111
  4. J.S. Park, Y.C. Kwun, and J.H. Park, "A fixed point theorem in the intuitionistic fuzzy metric spaces," Far East Journal of Mathematical Sciences. vol. 16, no. 2, pp. 137-149, Feb. 2005.
  5. J.S. Park, J.H. Park, and Y.C. Kwun, "Fixed point theorems in intuitionistic fuzzy metric space(I)", JP Journal of fixed point Theory and Applications, vol. 2, no. 1, pp. 79-89, 2007.
  6. J.S. Park, "Common fixed point for compatible mappings of type(${\alpha}$) on intuitionistic fuzzy metric space with implicit relations," Honam Mathematical Journal, vol. 32, no. 4, pp. 663-673, Dec. 2010. http://dx.doi.org/10.5831/HMJ.2012.34.1.77
  7. J.S. Park, "Some common fixed points for type(${\beta}$) compatible maps in an intuitionistic fuzzy metric space," International Journal of Fuzzy Logic and Intelligent Systems, vol. 13, no. 2, pp. 147-153, Jun. 2013. http://dx.doi.org/10.5391/IJFIS.2013.13.2.147
  8. J.S. Park, J.H. Park, and Y.C. Kwun, "On some results for five mappings using compatibility of type(${\alpha}$) in intuitionistic fuzzy metric space", International Journal of Fuzzy Logic and Intelligent Systems, vol. 8, no. 4, pp. 299-305, Dec. 2008. http://dx.doi.org/10.5391/IJFIS.2008.8.4.299
  9. J. H. Park, J. S. Park, and Y. C. Kwun, "Fixed points in M-fuzzy metric spaces," Fuzzy Optimization and Decision Making, vol. 7, no. 4, pp. 305-315, Dec. 2008. http://dx. doi.org/10.1007/s10700-008-9039-9
  10. J. S. Park, "Fixed point theorems for weakly compatible functions using (JCLR) property in intuitionistic fuzzy metric space," International Journal of Fuzzy Logic and Intelligent Systems, vol. 12, no. 4, pp. 296-299, Dec. 2012. http://dx.doi.org/10.5391/IJFIS.2012.12.4.296
  11. J. S. Park, "Some fixed point theorems using compatible maps in intuitionistic fuzzy metric space," International Journal of Fuzzy Logic and Intelligent Systems, vol. 11, no. 2, pp. 108-112, Jun. 2011. http://dx.doi.org/10.5391/IJFIS.2011.11.2.108
  12. J. S. Park, "On fixed point theorem of weak compatible maps of type(${\gamma}$) in complete intuitionistic fuzzy metric space," International Journal of Fuzzy Logic and In-telligent Systems, vol. 11, no. 1, pp. 38-43, Mar. 2011. http://dx.doi.org/10.5391/IJFIS.2011.11.1.038
  13. B. Schweizer and A. Sklar, "Statistical metric spaces," Pacific Journal of Mathematics, vol. 10, no. 1, pp. 313-334, 1960. https://doi.org/10.2140/pjm.1960.10.313
  14. J. H. Park, J. S. Park, and Y. C. Kwun, "A common fixed point theorem in the intuitionistic fuzzy metric space," in 2nd International Conference on Natural Computation, Xian, China, September 24-28, 2006, pp. 293-300.
  15. S. Sharma and B. Desphande, "Common fixed points of compatible maps of type(${\beta}$) on fuzzy metric spaces," Demonsratio Mathematics, vol. 35, pp. 165-174, 2002.
  16. M. Imbad, S. Kumar, and M. S. Khan, "Remarks on some fixed point theorems satisfying implicit relations," Radovi Mathematics, vol. 11, no. 1, pp. 135-143, 2002.