CFP last date
20 May 2024
Call for Paper
June Edition
IJCA solicits high quality original research papers for the upcoming June edition of the journal. The last date of research paper submission is 20 May 2024

Submit your paper
Know more
The week's pick
Responsive image
Enhancing Privacy Preservation: Multi-Attribute Protection with P-Sensitive K-Anonymity

Twinkle Patel Kiran Amin
Random Articles
Reseach Article

Common Fixed Point Theorems in Fuzzy Metric Space using Implicit Relation

by Asha Rani, Sanjay Kumar
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 20 - Number 7
Year of Publication: 2011
Authors: Asha Rani, Sanjay Kumar
10.5120/2459-3149

Asha Rani, Sanjay Kumar . Common Fixed Point Theorems in Fuzzy Metric Space using Implicit Relation. International Journal of Computer Applications. 20, 7 ( April 2011), 52-55. DOI=10.5120/2459-3149

@article{ 10.5120/2459-3149,
author = { Asha Rani, Sanjay Kumar },
title = { Common Fixed Point Theorems in Fuzzy Metric Space using Implicit Relation },
journal = { International Journal of Computer Applications },
issue_date = { April 2011 },
volume = { 20 },
number = { 7 },
month = { April },
year = { 2011 },
issn = { 0975-8887 },
pages = { 52-55 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume20/number7/2459-3149/ },
doi = { 10.5120/2459-3149 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:07:13.504282+05:30
%A Asha Rani
%A Sanjay Kumar
%T Common Fixed Point Theorems in Fuzzy Metric Space using Implicit Relation
%J International Journal of Computer Applications
%@ 0975-8887
%V 20
%N 7
%P 52-55
%D 2011
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this paper, we prove common fixed point theorems in fuzzy metric spaces for weakly compatible mappings along with property (E.A.) satisfying implicit relation. Property (E.A.) buys containment of ranges without any continuity requirement besides minimizing the commutativity conditions of the maps to commutativity at their point of coincidence. Moreover, property (E.A.) allows replacing the completeness requirement of the space with a more natural condition of closeness of the range.

References
  1. Aamri, M. and Moutawakil, D.El. 2002. Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl. 270, 181-188..
  2. Abbas, M., Altun, I., and Gopal, D. 2009. Common fixed point theorems for non compatible mappings in fuzzy metric spaces, Bull. Of Mathematical Analysis and Applications ISSN, 1821-1291, URL; http: // www. Bmathaa.org, Volume 1, Issue 2, 47-56.
  3. Aliouche, A. 2007. Common fixed point theorems via an implicit relation and new properties, Soochow Journal Of Mathematics, Voume 33, No. 4, pp. 593-601, October 2007.
  4. Cho, Y. J. , Sedghi, S., and Shobe, N. 2009. Generalized fixed point theorems for Compatible mappings with some types in fuzzy metric spaces, Chaos, Solitons and Fractals, 39, 2233-2244.
  5. George, A. , and Veeramani, P. 1997. On some results of analysis for fuzzy metric spaces,Fuzzy Sets and Systems, 90, 365-368.
  6. Jain, S., Mundra , B.,and Aake, S. 2009. Common fixed point theorem in fuzzy metric space using Implicit relation, Internat Mathematics Forum, 4, No. 3, 135 – 141.
  7. Jungck, G. 1996. Compatible mappings and common fixed points, Internat J. Math. Math. Sci. 9, 771-779.
  8. Kaleva, O., and Seikkala, S. 1984. On fuzzy metric spaces, Fuzzy Sets Systems 12, 215-229.
  9. Kramosil, O. , and Michalek, J. 1975. Fuzzy metric and statistical metric spaces, Kybernetika, 11, 326-334.
  10. Kubiaczyk and Sharma, S. 2008. Some common fixed point theorems in menger space under strict contractive conditions, Southeast Asian Bulletin of Mathematics 32: 117 – 124.
  11. Kumar, S. 2011. Fixed point theorems for weakly compatible maps under E.A. property in fuzzy metric spaces, J. Appl. Math. & Informatics Vol. 29, No. 1, pp. 395-405 Website: http://www.kcam.biz.
  12. Mishra, S. N., Sharma, N., and Singh, S. L. 1994. Common fixed points of maps in fuzzy metric spaces, Int. J. Math. Math. Sci.,17, 253-258.
  13. Pant, V. 2006. Contractive conditions and Common fixed points in fuzzy metric spaces, J. Fuzzy. Math., 14(2), 267-272.
  14. Popa, V. 2000. A general coincidence theorem for compatible multivalued mappings satisfying an implicit relation, Demonsratio Math., 33, 159-164.
  15. Popa, V. 1999. Some fixed point theorems for compatible mappings satisfying on implicit relation, Demonsratio Math., 32, 157 – 163.
  16. Regan, D. O`, and Abbas, M. Necessary and sufficient conditions for common fixed point theorems in fuzzy metric spaces, Demonstratio Mathematica, to appear.
  17. Schweizer, B. , and Sklar, A. 1960. Statistical metric spaces, Pacific J. Math., 10, 313-334.
  18. Sharma, S. 2002. Common fixed point theorems in fuzzy metric spaces, Fuzzy Sets and Systems, 127, 345 – 352.
  19. Singh, B., and Chauhan, M.S. 2000. Common fixed points of compatible maps in fuzzy metric spaces, Fuzzy Sets and Systems, 115, 471-475.
  20. Turkoglu, D. , and Rhoades, B. E. 2005. A fixed fuzzy point for fuzzy mapping in complete metric spaces , Math. Communications, 10(2), 115-121.
  21. Vasuki, R. 1999. Common fixed points for R-weakly commuting maps in fuzzy metric spaces, Indian J. Pure Appl. Math. 30, 419-423.
  22. Zadeh, L. A. 1965. Fuzzy sets, Inform. Acad Control, 8, 338-353.
Index Terms

Computer Science
Information Sciences

Keywords

Common fixed point Weakly compatible maps property (E.A.)

Powered by PhDFocusTM