Pure and Applied Mathematics Journal 2015; 4(4): 155-158 Published online July 25, 2015 (http://www.sciencepublishinggroup.com/j/pamj) doi: 10.11648/j.pamj.20150404.13 ISSN: 2326-9790 (Print); ISSN: 2326-9812 (Online) Fixed Point Theorems for Occasionally Weakly Compatible Maps in Intuitionistic Fuzzy Semi- Metric Space Harpreet Kaur 1 , Saurabh Manro 2 1 Department of Mathematics, Desh Bhagat University, Mandi Gobindgarh, India 2 School of Mathematics and Computer Applications, Thapar University, Patiala, India Email address: sauravmanro@hotmail.com (S. Manro) To cite this article: Harpreet Kaur, Saurabh Manro. Fixed Point Theorems for Occasionally Weakly Compatible Maps in Intuitionistic Fuzzy Semi- Metric Space. Pure and Applied Mathematics Journal. Vol. 4, No. 4, 2015, pp. 155-158. doi: 10.11648/j.pamj.20150404.13 Abstract: In this paper, using the concept of occasionally weakly compatible maps, we prove common fixed point theorems for two maps and pairs of maps in intuitionistic fuzzy semi-metric space. Example is also given to prove the validity of proved results. Our results extends and generalizes various known fixed point theorems in the setting of metric, fuzzy, intuitionistic fuzzy and modified fuzzy metric spaces. Keywords: Intuitionistic Fuzzy Semi- Metric Space, Occasionally Weakly Compatible Maps, Weakly Compatible Maps 1. Introduction Atanassove[2] introduced and studied the concept of intuitionistic fuzzy sets as a generalization of fuzzy sets. In 2004, Park[13] 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.[1] 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[6] . In 2006, Turkoglu[14] proved Jungck’s[4] common fixed point theorem in the setting of intuitionistic fuzzy metric spaces for commuting mappings. Later, various authors (see, [7-12]) proved various fixed point theorems in the setting of intuitionistic fuzzy metric space. In this paper, using the concept of occasionally weakly compatible maps, we prove common fixed point theorems for two maps and pairs of maps in intuitionistic fuzzy semi-metric space. Example is also given to prove the validity of proved results. Our results extends and generalizes various known fixed point theorems (see, [3], [5]) in the setting of metric, fuzzy, intuitionistic fuzzy and modified fuzzy metric spaces. 2. Preliminaries The concepts of triangular norms (t –norm) and triangular conorms (t- conorm) are known as the axiomatic skelton that we use are characterization fuzzy intersections and union respectively. These concepts were originally introduced by Menger in study of statistical metric spaces. Definition 2.1:[1] A binary operation * : [0,1]×[0,1] → [0,1] is continuous t-norm if * is satisfies the following conditions: for all a, b, c, d ∈ [0, 1], (i) * is commutative and associative; (ii) * is continuous; (iii) a * 1 = a; (iv) a * b ≤ c * d whenever a ≤ c and b ≤ d. Definition 2.2:[1] A binary operation ◊ : [0,1]×[0,1] → [0,1] is continuous t-conorm if ◊ is satisfies the following conditions: for all a, b, c, d ∈ [0, 1], (i) ◊ is commutative and associative; (ii) ◊ is continuous; (iii) a ◊ 0 = a; (iv) a ◊ b ≤ c ◊ d whenever a ≤ c and b ≤ d. Alaca et al.[1] defined the notion of intuitionistic fuzzy metric space as follows : Definition 2.3: A 5-tuple (X, M, N, *, ◊) is said to be an intuitionistic fuzzy metric space if X is an arbitrary set, * is a continuous t-norm, ◊ is a continuous t-conorm and M, N are fuzzy sets on X 2 ×[0, ∞) satisfying the following conditions: for all x, y, z ∈ X and s, t > 0, (i) M(x, y, t) + N(x, y, t) ≤ 1; (ii) M(x, y, 0) = 0;