Common Fixed Point Theorem in Fuzzy Metric Spaces Under E. A. Like Property

George and Veeramani [1] modify the concept of fuzzy metric spaces introduced by Kramosil and Michalek [4], Aamri and Moutawakil [8] generalized the notion of non-compatible mapping in metric space by E.A. property.Continuing the above conceptwe prove some commonfixed point theorem for a pair of weakly compatible maps under E.A. Like property.


Introduction
Fuzzy set theory has various applications in different area. When the notion of fuzzy set was introduced, then it was the turning point in the development of mathematics. It was introduced by Zadeh [7]. Fuzzy set theory has various application in applied science such as neural network theory, stability theory, mathematical programming, modelling theory, engineering science, medical science etc.George and Veeramani [1] modify the concept of fuzzy metric spaces introduced by Kramosil and Michalek [4],with a view to obtain a Hausdorff topology on fuzzy metric spaces, continuously, many authors gives very important results a Sessa [14], Vasuki [12] etc. Aamri and Moutawakil [8] generalized the notion of non-compatible mapping in metric space by E.A. property.It was pointed out in [9] that property E.A. buys containment of ranges without any continuity requirement besides minimizes the commutatively at their point of coincidence. In this paper, we establish some new results in common fixed point theorems in fuzzy metric spaces under E. A. Like [6].  , Then ( , % , , * ) is a fuzzy metric space. We call this fuzzy metric induced by a metric d as the standard intuitionistic fuzzy metric. Definition 2.5 Two self-mappings $and1 of a fuzzy metric space ( , %, * ) are called compatible if 2 3→4 %($1 3 , 1$ 3 , ") = 1 whenever { 3 } is a sequence in X such that 2 3→4 $ 3 = 2 3→4 1 3 = for some ∈ . Lemma 2.6 Let ( , %, * ) be fuzzy metric space. If there exists 5 ∈ (0,1) such that %( , , 5") ≥ %( , , ") for all , ∈ and " > 0, then = . Definition 2.7 Let be a set, $ and 1 self maps of . A point ∈ is called a coincidence point of $ and 1 iff $ = 1 . We shall call 7 = $ = 1 a point of coincidence of $and 1.

Definition
Definition 2.8 [3] A pair of maps 8 and 9 is called weakly compatible pair if they commute at coincidence points. Definition 2.9 Let $ and 1 be two self-maps of a fuzzy metric space( , %, * ).we say that $and 1 satisfy the property E. A. if there exists a sequence { 3 } such that, 2 3→4 $ 3 = 2 3→4 1 3 = for some ∈ .
(2) It minimizes the commutativity conditions of the maps to the commutativity at their points of coincidence.
(3) It allows replacing the completeness requirement of the space with a more natural condition of closeness of the range.
Of course, if two mappings satisfy E. A. like property then they satisfy E. A. property also, but, on the other hand, E. A. like property relaxes the condition of containment of ranges and closeness of the ranges to prove common fixed point theorems, which are necessary with E. A. property. Which is a contradiction. Hence $ = 1 = . Hence is a common fixed point of $and 1.