Common Fixed Point Theorems in Manger Space for Six Self Mappings Using an Implicit Relation and CLR/JCLR-property


  • L.H. Nagaraja Rao
  • S. Rajesh


The aim of this paper is to prove, mainly, three common xed
point theorems for six self mappings of a Menger space using two weakly compatible pairs having CLR/JCLR-property and satisfying an implicit relation. These generalize several known results including those of Kohli et. al.


[1] C. Sunny, S. Wutiphol and K. Poom. Common Fixed point theorems for weakly compatible mappings in fuzzy metric space using (JCLR) property, Applied Mathematics, 3(2012), 976-

[2] J. K. Kohli, S. Vashistha and D. Kumar. A Common Fixed point theorem for six mappings in Probabilistic metric spaces satisfying contractive type implicit relations, Int. J. Math.
Anal., 4(2)(2010), 63-74.

[3] S. Kumar and B. D. Pant. Common Fixed point theorem in Probabilistic metric space using implicit relation, Filomat, 22(2)(2008), 43-52.

[4] K. Menger. Statistical Metrices, Proceedings of the National Academy of Sciences of the United States of America, 28(12)(1942), 535-537.

[5] S. N. Mishra. Common fixed point theorem of compatible mappings in probabilistic metric spaces, Math. Japan, 36(2)(1991), 283-289.

[6] I. H. Nagaraja Rao, S. Rajesh and G. Venkata Rao. Common xed point theorems in Menger space for six self maps using an implicit relation, Bull. Int. Math. Virtual Inst., 4(1)(2014), 89-96.

[7] B. D. Pant and S. Chauhan. Common Fixed point theorems for semi-compatible mappings using implicit relasion, Int. J. Math. Analysis, 3(28)(2009), 1389-1398.

[8] B. Schweizer and A. Sklar. Probabilistic Metric Spaces, North Hooland Amsferdam, 1983.

[9] S. Singh and S. Jain, A Fixed point theorem in Menger spaces through weakly compatibility, J. Math. Anal. Appl., 301(2005), 439-448.

[10] S. Wutiphol and K. Poom. Common Fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces, J. Appl. Math., 2011 (2011), Article ID 637958.