Common Fixed Point Theorem for Weakly Compatible Maps in Intuitionistic Fuzzy Metric Spaces using Implicit Relation

Saurabh Manro

doi:10.15415/mjis.2014.22017

Authors

Saurabh Manro School of Mathematics and Computer Applications, Thapar University, Patiala, Punjab

DOI:

https://doi.org/10.15415/mjis.2014.22017

Keywords:

Intuitionistic fuzzy metric space, property E.A, implicit relation

Abstract

In this paper, we use the notion of property E.A. in an intuitionistic fuzzy metric space to prove a common fixed point theorem which generalizes Theorem-2 of Turkoglu et al. (2006).

Downloads

Download data is not yet available.

References

Aamri, M. and Moutawakil, D. El. (2002), ‘Some new common fixed point theorems under strict contractive conditions’, J. Math. Anal. Appl., 270, pp.181-188.

http://dx.doi.org/10.1016/S0022-247X(02)00059-8

Alaca, C., Turkoglu, D. and Yildiz C. (2006), ‘Fixed points in Intuitionistic fuzzy metric spaces’, Chaos, Solitons & Fractals, 29, pp.1073-1078. http://dx.doi.org/10.1016/j.chaos.2005.08.066

Atanassov, K.(1986), Intuitionistic Fuzzy sets, Fuzzy sets and system, 20, pp.87-96. http://dx.doi.org/10.1016/S0165-0114(86)80034-3

Coker, D.(1997), ‘An introduction to Intuitionistic Fuzzy topological spaces’, Fuzzy Sets and System, 88, pp. 81- 89. http://dx.doi.org/10.1016/S0165-0114(96)00076-0

Grorge, A. and Veeramani P.(1994), ‘On some results in fuzzy metric spaces’, Fuzzy Sets and Systems, 64, pp. 395- 399. http://dx.doi.org/10.1016/0165-0114(94)90162-7

Jungck, G.(1976), ‘Commuting mappings and fixed points’, Amer. Math. Monthly, 83, pp. 261-263. http://dx.doi.org/10.2307/2318216

Kramosil, I. and Michalek, J.(1975), ‘Fuzzy metric and Statistical metric spaces’, Kybernetica,11, pp.326-334.

Manro, S., Kumar, S. and Singh, S.(2010), ‘Common fixed point theorems in intuitionistic fuzzy metric spaces’, Applied Mathematics,1, pp.510-514.

http://dx.doi.org/10.4236/am.2010.16067

Manro, S., Bouharjera, H. and Singh, S.(2010), ‘A common fixed point theorem in intuitionistic fuzzy metric space by using sub-compatible maps’, Int. J. Contemp. Math. Sciences, 5(55), pp. 2699 – 2707.

Manro, S., Bhatia, S. S., and Kumar, S. (2010), ‘Common fixed point theorem for weakly compatible maps satisfying E.A. property in intuitionistic fuzzy metric spaces’, Punjab

University Journal of Mathematics, 42, pp. 51-56.

Manro, S., Kumar, S. and Bhatia, S.S.(2012), ‘Common fixed point theorems in Intuitionistic fuzzy metric spaces using occasionally weakly compatible maps’, J. Math. Comput. Sci., 2(2), pp.73-81.

Manro, S., Bhatia, S. S., and Kumar, S. (2012), ‘Common fixed point theorems for weakly compatible maps satisfying common (E.A.) property in intuitionistic fuzzy metric spaces using implicit relation’, Journal of Advanced Studies in Topology, 3(2), pp. 38-44.

Manro, S., Kumar, S., Kumar, S. and Bhatia, S. S.(2012), ‘Common fixed point theorem in intuitionistic fuzzy metric spaces using common (E.A) property and implicit relation’,

Journal of Advanced Studies in Topology, 3(3), pp. 60-68.

Park, J. H. (2004), ‘Intuitionistic fuzzy metric spaces’, Chaos, Solitons & Fractals, 22, pp.1039-1046. http://dx.doi.org/10.1016/j.chaos.2004.02.051

Park, J.S., Kwun, Y.C. and Park, J.H.(2005), ‘A fixed point theorem in the Intuitionistic fuzzy metric spaces’, Far East J. Math. Sci., 16, pp. 137-149.

Saadati R. and Park J.H.(2006), ‘On the Intuitionistic fuzzy topological spaces’, Chaos, Solitons & Fractals, 27, pp. 331-344. http://dx.doi.org/10.1016/j.chaos.2005.03.019

Schweizer, B. and Sklar, A. (1960), ‘Statistical metric spaces’, Pacific J. Math., 10, pp. 313-334. http://dx.doi.org/10.2140/pjm.1960.10.673

Turkoglu D., Alaca C., Cho Y.J. and Yildiz C.(2006), ‘Common fixed point theorems in Intuitionistic fuzzy metric spaces’, J. Appl. Math. & Computing, 22, pp. 411-424.

http://dx.doi.org/10.1007/BF02896489