Common fixed point theorems in intuitionistic fuzzy metric spaces and -fuzzy metric spaces with nonlinear contractive condition

The purpose of this paper is to prove some common fixed point theorems for a pair of R-weakly commuting mappings defined on intuitionistic fuzzy metric spaces [Park JH. Intuitionistic fuzzy metric spaces. Chaos, Solitons & Fractals 2004;22:1039–46] and -fuzzy metric spaces [Saadati R, Razani A, Adibi H. A common fixed point theorem in -fuzzy metric spaces. Chaos, Solitons & Fractals, doi:10.1016/j.chaos.2006.01.023], with nonlinear contractive condition, defined with function, first observed by Boyd and Wong [Boyd DW, Wong JSW. On nonlinear contractions. Proc Am Math Soc 1969;20:458–64]. Following Pant [Pant RP. Common fixed points of noncommuting mappings. J Math Anal Appl 1994;188:436–40] we define R-weak commutativity for a pair of mappings and then prove the main results. These results generalize some known results due to Saadati et al., and Jungck [Jungck G. Commuting maps and fixed points. Am Math Mon 1976;83:261–3]. Some examples and comments according to the preceding results are given.