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TRIPLED COINCIDENCE POINT THEOREM IN FUZZY METRIC SPACES

Year 2017, Volume: 5 Issue: 1, 223 - 231, 03.04.2017

Abstract

In this article we prove some common tripled xed point theorems for contractive mappings in fuzzy metric spaces under geometrically convergent t-norms. Our aim of this paper is to improve the result of A. Gupta, R. Narayan and R. N. Yadava, Tripled Fixed Point For Compatible Mappings In Partially Ordered Fuzzy Metric Spaces, The Journal Of Fuzzy Mathematics 22(3), 565-580, 2014. Our technique for the proof of the theorem is di erent. We also give an example in support of our theorem.

References

  • 1. Aydi H., Karapınar E., Postolache M., Tripled coincidence point theorems for weak- contractions in partially ordered metric spaces. Fixed Point Theory Appl. 2012, 44 (2012).
  • 2. Berinde V., Borcut M., Tripled xed point theorems for contractive type mappings in partially ordered metric spaces. Nonlinear Anal. 74 (15)(2011), 4889-4897.
  • 3. Ciric L. , Mihet D., Saadati R., Monotone generalized contractions in partially ordered probabilistic metric spaces, Topology and its Applications 156 (2009), 2838-2844.
  • 4. Ciric L., Agarwal R., Samet B., Mixed monotone-generalized contractions in partially ordered probabilistic metric spaces, Fixed Point Theory and Applications 2011, 2011:56 doi:10.1186/1687-1812-2011-56.
  • 5. El-Ghoul M., El-Zohny H., and Radwan S., Fuzzy incidence matrix of fuzzy simplicial complexes and its folding, Chaos, Solitons & Fractals, 13(9)(2002), 1827-1833.
  • 6. El-Sayied H. K., Study on generalized convex fuzzy bodies, Applied Mathematics and Computation, 152 (1) 2004, 245-252.
  • 7. Fang J.X., Common Fixed point theorems of compatible and weakly compatible maps in Menger spaces, Nonlinear Analysis. Theory, Methods & Applications 71 (2009), 1833-1843.
  • 8. Gupta A., Narayan R. and Yadava R. N., "Tripled Fixed Point For Compatible Mappings In Partially Ordered Fuzzy Metric Spaces," The Journal Of Fuzzy Mathematics 22(3)(2014), 565-580.
  • 9. Hadzic O., Pap E., Fixed Point Theory in Probabilistic Metric Spaces, Kluwer Academic Publishers, Dordrecht, 2001.
  • 10. Hadzic O., Pap E., Budincevic M., Countable extension of triangular norms and their applications to the xed point theory in probabilistic metric spaces, Kybernetika 38 (3) (2002), 363-381.
  • 11. Hu X.Q., Common Coupled Fixed Point Theorems for Contractive Mappings in Fuzzy Metric Spaces, Fixed Point Theory and Applications Volume 2011, Article ID 363716, doi:10.1155/2011/363716.
  • 12. Hu X. Q., Ma X.Y., Coupled coincidence point theorems under contractive conditions in partially ordered probabilistic metric spaces, Nonlinear Analysis. Theory, Methods & Applications 74 (2011), 6451-6458.
  • 13. Kramosil I., Michalek J., Fuzzy metrics and statistical metric spaces, Kybernetika 11 (1975), 336-344.
  • 14. Lakshmikantham V., Ciric L., Coupled xed point theorems for nonlinear contractions in par tially ordered metric spaces, Nonlinear Analysis. Theory, Methods & Applications 70 (2009), 4341-4349.
  • 15. Sedghi S., Altun I., Shobe N., Coupled xed point theorems for contractions in fuzzy metric spaces, Nonlinear Analysis. Theory, Methods & Applications 72 (2010), 1298-1304.
  • 16. Roldan A., Moreno J. M., Roldan C. , Tripled xed point theorem in fuzzy metric spaces and applications , Fixed point theory and applications, doi: 10.1186/1687-1812-2013-29.
  • 17. Zadeh L. A. , Fuzzy sets, Information and Control, 8(1965),338-353.
  • 18. Zhu X.H., Xiao J.Z., Note on "Coupled xed point theorems for contractions in fuzzy metric spaces", Nonlinear analysis. Theory, Methods & Applications 74 (2011), 5475-5479.
Year 2017, Volume: 5 Issue: 1, 223 - 231, 03.04.2017

Abstract

References

  • 1. Aydi H., Karapınar E., Postolache M., Tripled coincidence point theorems for weak- contractions in partially ordered metric spaces. Fixed Point Theory Appl. 2012, 44 (2012).
  • 2. Berinde V., Borcut M., Tripled xed point theorems for contractive type mappings in partially ordered metric spaces. Nonlinear Anal. 74 (15)(2011), 4889-4897.
  • 3. Ciric L. , Mihet D., Saadati R., Monotone generalized contractions in partially ordered probabilistic metric spaces, Topology and its Applications 156 (2009), 2838-2844.
  • 4. Ciric L., Agarwal R., Samet B., Mixed monotone-generalized contractions in partially ordered probabilistic metric spaces, Fixed Point Theory and Applications 2011, 2011:56 doi:10.1186/1687-1812-2011-56.
  • 5. El-Ghoul M., El-Zohny H., and Radwan S., Fuzzy incidence matrix of fuzzy simplicial complexes and its folding, Chaos, Solitons & Fractals, 13(9)(2002), 1827-1833.
  • 6. El-Sayied H. K., Study on generalized convex fuzzy bodies, Applied Mathematics and Computation, 152 (1) 2004, 245-252.
  • 7. Fang J.X., Common Fixed point theorems of compatible and weakly compatible maps in Menger spaces, Nonlinear Analysis. Theory, Methods & Applications 71 (2009), 1833-1843.
  • 8. Gupta A., Narayan R. and Yadava R. N., "Tripled Fixed Point For Compatible Mappings In Partially Ordered Fuzzy Metric Spaces," The Journal Of Fuzzy Mathematics 22(3)(2014), 565-580.
  • 9. Hadzic O., Pap E., Fixed Point Theory in Probabilistic Metric Spaces, Kluwer Academic Publishers, Dordrecht, 2001.
  • 10. Hadzic O., Pap E., Budincevic M., Countable extension of triangular norms and their applications to the xed point theory in probabilistic metric spaces, Kybernetika 38 (3) (2002), 363-381.
  • 11. Hu X.Q., Common Coupled Fixed Point Theorems for Contractive Mappings in Fuzzy Metric Spaces, Fixed Point Theory and Applications Volume 2011, Article ID 363716, doi:10.1155/2011/363716.
  • 12. Hu X. Q., Ma X.Y., Coupled coincidence point theorems under contractive conditions in partially ordered probabilistic metric spaces, Nonlinear Analysis. Theory, Methods & Applications 74 (2011), 6451-6458.
  • 13. Kramosil I., Michalek J., Fuzzy metrics and statistical metric spaces, Kybernetika 11 (1975), 336-344.
  • 14. Lakshmikantham V., Ciric L., Coupled xed point theorems for nonlinear contractions in par tially ordered metric spaces, Nonlinear Analysis. Theory, Methods & Applications 70 (2009), 4341-4349.
  • 15. Sedghi S., Altun I., Shobe N., Coupled xed point theorems for contractions in fuzzy metric spaces, Nonlinear Analysis. Theory, Methods & Applications 72 (2010), 1298-1304.
  • 16. Roldan A., Moreno J. M., Roldan C. , Tripled xed point theorem in fuzzy metric spaces and applications , Fixed point theory and applications, doi: 10.1186/1687-1812-2013-29.
  • 17. Zadeh L. A. , Fuzzy sets, Information and Control, 8(1965),338-353.
  • 18. Zhu X.H., Xiao J.Z., Note on "Coupled xed point theorems for contractions in fuzzy metric spaces", Nonlinear analysis. Theory, Methods & Applications 74 (2011), 5475-5479.
There are 18 citations in total.

Details

Subjects Engineering
Journal Section Articles
Authors

ANIMESH Gupta This is me

J. K. Maıtra This is me

Publication Date April 3, 2017
Submission Date April 3, 2017
Acceptance Date December 12, 2016
Published in Issue Year 2017 Volume: 5 Issue: 1

Cite

APA Gupta, A., & Maıtra, J. K. (2017). TRIPLED COINCIDENCE POINT THEOREM IN FUZZY METRIC SPACES. Konuralp Journal of Mathematics, 5(1), 223-231.
AMA Gupta A, Maıtra JK. TRIPLED COINCIDENCE POINT THEOREM IN FUZZY METRIC SPACES. Konuralp J. Math. April 2017;5(1):223-231.
Chicago Gupta, ANIMESH, and J. K. Maıtra. “TRIPLED COINCIDENCE POINT THEOREM IN FUZZY METRIC SPACES”. Konuralp Journal of Mathematics 5, no. 1 (April 2017): 223-31.
EndNote Gupta A, Maıtra JK (April 1, 2017) TRIPLED COINCIDENCE POINT THEOREM IN FUZZY METRIC SPACES. Konuralp Journal of Mathematics 5 1 223–231.
IEEE A. Gupta and J. K. Maıtra, “TRIPLED COINCIDENCE POINT THEOREM IN FUZZY METRIC SPACES”, Konuralp J. Math., vol. 5, no. 1, pp. 223–231, 2017.
ISNAD Gupta, ANIMESH - Maıtra, J. K. “TRIPLED COINCIDENCE POINT THEOREM IN FUZZY METRIC SPACES”. Konuralp Journal of Mathematics 5/1 (April 2017), 223-231.
JAMA Gupta A, Maıtra JK. TRIPLED COINCIDENCE POINT THEOREM IN FUZZY METRIC SPACES. Konuralp J. Math. 2017;5:223–231.
MLA Gupta, ANIMESH and J. K. Maıtra. “TRIPLED COINCIDENCE POINT THEOREM IN FUZZY METRIC SPACES”. Konuralp Journal of Mathematics, vol. 5, no. 1, 2017, pp. 223-31.
Vancouver Gupta A, Maıtra JK. TRIPLED COINCIDENCE POINT THEOREM IN FUZZY METRIC SPACES. Konuralp J. Math. 2017;5(1):223-31.
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