Cemil Yildiz

Common fixed point theorems in intuitionistic fuzzy metric spaces

The purpose of this paper, using the idea of intuitionistic fuzzy set due to Atanassov [2], we define the notion of intuitionistic fuzzy metric spaces (see, [1]) due to Kramosil and Michalek [17] and Jungck’s common fixed point theorem ([11]) is generalized to intuitionistic fuzzy metric spaces. Further, we first formulate the definition of weakly commuting and R-weakly commuting mappings in intuitionistic fuzzy metric spaces and prove the intuitionistic fuzzy version of Pant’s theorem ([21]).

Compatible Maps and Compatible Maps of Types (α) and (β) in Intuitionistic Fuzzy Metric Spaces

In this paper, we first formulate the definition of compatible maps and compatible maps of types (a) and (/3) in intuitionistic fuzzy metric spaces and give some relations between the concepts of compatible maps and compatible maps of types (a) and 03). Introduction In 1965, the concept of fuzzy sets was introduced by Zadeh [25]. Since then many authors have expansively developed the theory of fuzzy sets and applications. Especially, Deng [5], Erceg [7], Kaleva and Seikkala [15], Kramosil and Michalek [18] have introduced the concepts of fuzzy metric space in different ways. George and Veeramani [8, 9] modified the concept of fuzzy metric spaces introduced by Kramosil and Michalek and defined the Hausdorff topology of fuzzy metric spaces. They showed also that every metric induces a fuzzy metric. Grabiec [10] extended the well known fixed point theorem of Banach and Edelstein [6] to fuzzy metric spaces in the sense of Kramosil and Michalek. Grabiec and Kramosil and Michalek, Mishra et al. [20] and many authors [11-14, 20, 22, 24] obtained common fixed point theorems for compatible maps and asymptotically commuting maps on fuzzy metric spaces, which generalize, extend and fuzzify several fixed point theorems for contractivetype maps on metric spaces and other spaces. Cho et al. [3] first formulate the definition of compatible maps of type (/3) in fuzzy metric spaces and give some relations between the concepts of compatible maps and compatible 1991 Mathematics Subject Classification: 54H25, 47H10.