Common fixed point for fuzzy mappings satisfying an implicit \(\varphi\)-contractive conditions in complete metric spaces

Volume 10, Issue 6, pp 3344--3356 http://dx.doi.org/10.22436/jnsa.010.06.43

Publication Date: June 26, 2017 Submission Date: July 10, 2016

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 1829 Downloads
• 2781 Views

Authors

Ming-Liang Song - Mathematics and Information Technology School, Jiangsu Second Normal University, Nanjing, 210013, P. R. China.

Abstract

In this paper, by using \(F_\varphi\)-type real functions, some common fixed point for fuzzy mappings satisfying an implicit \(\varphi\)- contractive conditions in complete metric spaces are established. Our results extend, generalize, and improve some existing results. Moreover, some applications and two examples are given here to illustrate the validity of the hypotheses of our main results.

Share and Cite

Keywords

• Common fixed point
• fuzzy mapping
• implicit \(\varphi\)-contractive condition
• multi-valued mappings
• complete metric space.

MSC

•  47H10
•  54H25
•  54A40
•  46A40

References

• [1] M. Abbas, B. Damjanović, R. Lazović, Fuzzy common fixed point theorems for generalized contractive mappings, Appl. Math. Lett., 23 (2010), 1326–1330.
  • View Article
  • MathSciNet
  • Google Scholar


• [2] M. Abbas, D. Turkoglu, Fixed point theorem for a generalized contractive fuzzy mapping, J. Intell. Fuzzy Systems, 26 (2014), 33–36.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [3] M. A. Ahmed, Fixed point theorems in fuzzy metric spaces, J. Egyptian Math. Soc., 22 (2014), 59–62.
  • View Article
  • Google Scholar


• [4] S. C. Arora, V. Sharma, Fixed point theorems for fuzzy mappings, Fuzzy Sets and Systems, 110 (2000), 127–130.


• [5] I. Beg, M. A. Ahmed, Fixed point for fuzzy contraction mappings satisfying an implicit relation , Mat. Vesnik, 66 (2014), 351–356.
  • MathSciNet
  • Google Scholar
  • MATH


• [6] J.-H. Chen, X.-J. Huang, Fixed point theorems for fuzzy mappings in metric spaces with an application, J. Inequal. Appl., 2015 (2015), 21 pages.
  • View Article
  • MathSciNet
  • Google Scholar


• [7] V. D. Estruch, A. Vidal, A note on fixed fuzzy points for fuzzy mappings, Proceedings of the ”II Italian-Spanish Congress on General Topology and its Applications” (Italian), Trieste, (1999), Rend. Istit. Mat. Univ. Trieste, 32 (2001), 39–45.
  • Google Scholar


• [8] S. Heilpern, Fuzzy mappings and fixed point theorem, J. Math. Anal. Appl., 83 (1981), 566–569.
  • View Article
  • Google Scholar


• [9] K. Iseki, Multi-valued contraction mappings in complete metric spaces, Rend. Sem. Mat. Univ. Padova, 53 (1975), 15–19.
  • MathSciNet
  • Google Scholar


• [10] B. S. Lee, S. J. Cho, A fixed point theorem for contractive-type fuzzy mappings, Fuzzy Sets and Systems, 61 (1994), 309–312.
  • View Article
  • MathSciNet
  • Google Scholar


• [11] S. B. Nadler, Jr., Multi-valued contraction mappings, Pacific J. Math., 30 (1968), 369–380.


• [12] J. Y. Park, J. U. Jeong, Common fixed points of fuzzy mappings, Fuzzy Sets and Systems, 59 (1993), 231–235.


• [13] J. Y. Park, J. U. Jeong, Fixed point theorems for fuzzy mappings, Fuzzy Sets and Systems, 87 (1997), 111–116.


• [14] R. A. Rashwan, M. A. Ahmed, Common fixed point theorems for fuzzy mappings, Arch. Math. (Brno), 38 (2002), 219–226.
  • Google Scholar


• [15] S. Sedghi, N. Shobe, I. Altun, A fixed fuzzy point for fuzzy mappings in complete metric spaces, Math. Commun., 13 (2008), 289–294.
  • MathSciNet
  • Google Scholar


• [16] K. L. Singh, J. H. M. Whitfield, Fixed points for contractive type multivalued mappings, Math. Japon., 27 (1982), 117–124.
  • Google Scholar


• [17] T. Som, R. N. Mukherjee, Some fixed point theorems for fuzzy mappings, Fuzzy Sets and Systems, 33 (1989), 213–219.
  • View Article
  • Google Scholar


• [18] M.-L. Song, X.-J. Zhang, Common fixed point theorems for Lipschitz-type fuzzy mappings in metric spaces, Fixed point Theory Appl., 2013 (2013), 14 pages.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH