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Reseach Article

Common Fixed Point Theorem in Sequentially Compact Intuitionistic Fuzzy Metric Spaces under Implicit Relations

by Seema Mehra
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 55 - Number 15
Year of Publication: 2012
Authors: Seema Mehra
10.5120/8831-2984

Seema Mehra . Common Fixed Point Theorem in Sequentially Compact Intuitionistic Fuzzy Metric Spaces under Implicit Relations. International Journal of Computer Applications. 55, 15 ( October 2012), 18-25. DOI=10.5120/8831-2984

@article{ 10.5120/8831-2984,
author = { Seema Mehra },
title = { Common Fixed Point Theorem in Sequentially Compact Intuitionistic Fuzzy Metric Spaces under Implicit Relations },
journal = { International Journal of Computer Applications },
issue_date = { October 2012 },
volume = { 55 },
number = { 15 },
month = { October },
year = { 2012 },
issn = { 0975-8887 },
pages = { 18-25 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume55/number15/8831-2984/ },
doi = { 10.5120/8831-2984 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:57:20.384215+05:30
%A Seema Mehra
%T Common Fixed Point Theorem in Sequentially Compact Intuitionistic Fuzzy Metric Spaces under Implicit Relations
%J International Journal of Computer Applications
%@ 0975-8887
%V 55
%N 15
%P 18-25
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

The aim of this paper is to introduce the notion of sequentially compact intuitionistic fuzzy metric spaces and prove a common fixed point theorem for pairs of weakly compatible self mappings in this newly defined space.

References
  1. Alaca, C. , Turkoglu, D. and Yildiz, C. , Fixed points in intuitionistic fuzzy metric spaces,Chaos, Solitons and Fractals, 29(2006), 1073- 1078.
  2. Atanassov, K. , Intuitionistic fuzzy sets, Fuzzy sets and systems 20(1986) 87-96.
  3. Dubois, D. and Prade, H. , Fuzzy Sets: Theory and Applications to Policy Analysis and Information Systems Plenum Press, New York, 1980.
  4. George, A. and Veeramani, P. , On some results in fuzzy metric space, Fuzzy Sets and Systems, 64(1994), 395-399.
  5. Grabiec, M. , Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems 27 ( 1988), 385-389.
  6. Jungck, G. and Rhoades,B. E, Fixed point for set valued functions without continuity, Indian. J. Pure & Applied Math. ,29(3), 1998,227-238.
  7. Klement, E. P. , Operations on fuzzy sets: an axiomatic approach, Inform. Sci. 27 (1984), 221-232.
  8. Klement, E. P. , Mesiar, R. and Pap, E. , A characterization of the ordering of continuous t-norms, Fuzzy Sets and Systems 86 (1997), 189-195.
  9. Klement, E. P. , Mesiar, R. and Pap, E. , Triangular Norms, Kluwer Academic Publ. , Trendsin Logic 8, Dordrecht 2000.
  10. Kramosil, O. and Michalek, J. , Fuzzy metric and statistical metric spaces, Kybernetica , 11 (1975), 326-334.
  11. Menger, K. , Statistical metrics, Proc. Nat. Acad. Sci. 28 (1942), 535-537.
  12. Park, J. H. , Intuitionistic Fuzzy Metric Spaces, Chaos, Solitons and Fractals, 22(2004) 1039-1046.
  13. Rao, K. P. R. , Rao, K. R. K. and Rao, T. Ranga, Common fixed point theorems in Sequentially Compact fuzzy metric spaces, International Mathematical Forum, 2(51)(2007)2543-2549.
  14. Sedghi, S. , Common fixed point theorems for multivalued contractions, International Mathematical Forum, 2(31), (2007),1499-1506.
  15. Sharma, S. , Kutukcu, S. , and Rathore, R. S. , Common fixed point for multivalued mappings in intuitionistic fuzzy metric spaces, Korean Math. Soc. 22(3)(2007),391-399.
  16. Turkoglu, D. , Alaca, C. , Cho, Y. J. and Yildiz, C. , Common fixed point theorems in intuitionistic fuzzy metric spaces, J. Appl. Math. And Computing, 22(1-2)(2006), 411-424.
  17. Zadeh, L. A. , Fuzzy sets, Inform and Control 8 (1965), 338-353.
Index Terms

Computer Science
Information Sciences

Keywords

Intuitionistic fuzzy metric space sequentially compact intuitionistic fuzzy metric space compatible mappings weakly compatible mappings common fixed point