Kannan’s and Chatterjee’s type fixed point theorems in intuitionistic fuzzy metric space

Abstract

In [T. K. Samanta, S. Mohinta and I. H. Jebril, On fixed point theorems in intuitionistic fuzzy metric spaces:int. J. Open problems compt. Math, Vol.5, No2, (2012), 15–27] the authors raise an open problem that Kannan’s and Chatterjee’sfixed point theorems can be established with the help of (TS − IFλ) contractive mapping. In this paper we not only gave the answer to this problem but also obtain generalization of Kannan’s and Chatterjee’s fixed point theorem in intuitionistic fuzzy metric spaces with new contractive mapping IFCα. We also obtained generalization of Banach fixed point theorem of (TS-IF) contractive mapping. An example is also given to convince our results.In [T. K. Samanta, S. Mohinta and I. H. Jebril, On fixed point theorems in intuitionistic fuzzy metric spaces:int. J. Open problems compt. Math, Vol.5, No2, (2012), 15–27] the authors raise an open problem that Kannan’s and Chatterjee’sfixed point theorems can be established with the help of (TS − IFλ) contractive mapping. In this paper we not only gave the answer to this problem but also obtain generalization of Kannan’s and Chatterjee’s fixed point theorem in intuitionistic fuzzy metric spaces with new contractive mapping IFCα. We also obtained generalization of Banach fixed point theorem of (TS-IF) contractive mapping. An example is also given to convince our results.