Common Fixed Point Theorem for Weakly Compatible Maps Satisfying E.a. Property in Intuitionistic Menger Spaces

INTRODUCTION There have been a number of generalizations of metric spaces. One such generalization is Menger space introduced in 1942 by Menger[9] who used distribution functions instead of nonnegative real numbers as values of the metric. This space was expanded rapidly with the pioneering works of Schweizer and Sklar [11, 12]. Modifying the idea of Kramosil and Michalek [7], George and Veeramani [5] introduced fuzzy metric spaces which are very similar that of Menger space. Atanassove [3] introduced and studied the concept of intuitionistic fuzzy sets as a generalization of fuzzy sets. In 2004, Park[10] defined the notion of intuitionistic fuzzy metric space with the help of continuous t-norms and continuous t-conorms. Recently, in 2006, Alaca et al.[2] using the idea of Intuitionistic fuzzy sets, defined the notion of intuitionistic fuzzy metric space with the help of continuous t-norm and continuous t-conorms as a generalization of fuzzy metric space due to Kramosil and Michalek[8] . Kutukcu et. al [8] introduced the notion of intuitionistic Menger spaces with the help of t-norms and tconorms as a generalization of Menger space due to Menger [9]. Further they introduced the notion of Cauchy sequences and found a necessary and sufficient condition for an intuitionistic Menger space to be complete. On the other hand, Jungck [6] introduced the notion of compatible mappings in metric spaces. The concept of weakly compatible mappings is most general as each pair of compatible mappings is weakly compatible but the converse is not true. Recently, Amari and Moutawakil[1] introduced a generalization of non compatible maps as E.A. property. These observations motivated us to prove a common fixed point theorem for six weakly compatible maps in intuitionistic Menger spaces. In this paper, we use the notion of E.A. property in intuitionistic Menger space and prove a common fixed point theorem for weakly compatible mappings using this property. 2. Preliminaries: The concepts of triangular norms ( tnorm ) and triangular conorms ( tconorm ) are known as the axiomatic skelton that we use are characterization fuzzy intersections and union respectively. These concepts were originally introduced by Menger [8] in study of statistical metric spaces. Definition 2.1[11]: A binary operation * : [0,1]×[0,1]  [0,1] is continuous t-norm if * is satisfies the following conditions: (i) * is commutative and associative; (ii) * is continuous;