Common Fixed Point Theorem in Intuitionistic Fuzzy Metric Space Using R-Weakly Commuting Mappings

Saurabh Manro, Satwinder Singh Bhatia, Sanjay Kumar

Deenbandhu Chhotu Ram, University of Science and Technology, Murthal, India.
School of Mathematics and Computer Applications, Thapar University, Patiala, India.

DOI: 10.4236/am.2012.33036                

Abstract

In this paper, we prove a common fixed point theorem in Intuitionistic fuzzy metric space by using pointwise R-weak commutativity and reciprocal continuity of mappings satisfying contractive conditions.

Keywords

Intuitionistic Fuzzy Metric Space; Reciprocal Continuity; R-Weakly Commuting Mappings; Common Fixed Point Theorem

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	K. Atanassov, “Intuitionistic Fuzzy Sets,” Fuzzy Sets and System, Vol. 20, No. 1, 1986, pp. 87-96. doi:10.1016/S0165-0114(86)80034-3
[2]	J. H. Park, “Intuitionistic Fuzzy Metric Spaces,” Chaos, Solitons & Fractals, Vol. 22, No. 5, 2004, pp.1039-1046. doi:10.1016/j.chaos.2004.02.051
[3]	C. Alaca, D. Turkoglu and C. Yildiz, “Fixed Points in Intuitionistic Fuzzy Metric Spaces,” Chaos, Solitons & Fractals, Vol. 29, No. 5, 2006, pp. 1073-1078. doi:10.1016/j.chaos.2005.08.066
[4]	I. Kramosil and J. Michalek, “Fuzzy Metric and Statistical Metric Spaces,” Kybernetica, Vol. 11, No. 5, 1975, pp. 326-334.
[5]	D. Turkoglu, C. Alaca, Y. J. Cho and C. Yildiz, “Common Fixed Point Theorems in Intuitionistic Fuzzy Metric Spaces,” Journal of Applied Mathematics and Computing, Vol. 22, No. 1-2, 2006, pp. 411-424.
[6]	G. Jungck, “Commuting Mappings and Fixed Points,” American Mathematical Monthly, Vol. 83, No. 4, 1976, pp. 261-263. doi:10.2307/2318216
[7]	S. Manro, S. Kumar and S. Singh, “Common Fixed Point Theorems in Intuitionistic Fuzzy Metric Spaces,” Applied Mathematics, Vol. 1, No. 6, 2010, pp. 510-514.
[8]	S. Manro, H. Bouharjera and S. Singh, “A Common Fixed Point Theorem in Intuitionistic Fuzzy Metric Space by Using Sub-Compatible Maps,” International Journal of Contemporary Mathematical Sciences, Vol. 5, No. 55, 2010, pp. 2699-2707. http://m-hikari.com/ijcms-2010/53-56-2010/manroIJCMS53-56-2010.pdf
[9]	S. Muralisankar and G. Kalpana, “Common Fixed Point Theorems in Intuitionistic Fuzzy Metric Spaces Using Reneral Contractive Condition of Integral Type,” International Journal of Contemporary Mathematical Sciences, Vol. 4, No. 11, 2009, pp. 505-518. http://www.m-hikari.com/ijcms-password2009/9-12-2009/muralisankarIJCMS9-12-2009.pdf
[10]	D. Turkoglu, C. Alaca and C. Yildiz, “Compatible Maps and Compatible Maps of Type (α) and (β) in Intuitionistic Fuzzy Metric Spaces,” Demonstratio Mathematica, Vol. 39, No. 3, 2006, pp. 671-684. http://demmath.mini.pw.edu.pl/pdf/dm39_3.pdf
[11]	D. Turkoglu, C. Alaca and C. Yildiz, “Common Fixed Point Theorems of Compatible Maps in Intuitionistic Fuzzy Metric Spaces,” Southeast Asian Bulletin of Mathematics, Vol. 32, 2008, pp. 21-33. http://seams-bull-math.scnu.edu.cn/
[12]	C. Alaca, I. Altun and D. Turkoglu, “On Compatible Mappings of Type (I) and (II) in Intuitionistic Fuzzy Metric Spaces,” Communications of the Korean Mathematical Society, Vol. 23, No. 3, 2008, pp. 427-446. http://mathnet.or.kr/mathnet/thesis_file/14_C07-110.pdf
[13]	B. Schweizer and A. Sklar, “Probabilistic Metric Spaces,” North Holland Series in Probability and Applied Mathematics, North-Holland, New York, Vol. 16, 1983, pp. 54-77.