Journal of Advanced Studies in Topology eISSN: 2090-388X pISSN: 2090-8288 Vol. 3, No. 4, 2012, 53–61 c  2012 Modern Science Publishers www.m-sciences.com RESEARCH ARTICLE A Common Fixed Point Theorem for Sub Compatible and Sub Sequentially Continuous Maps in Intuitionistic Fuzzy Metric Spaces Using Implicit Relation Mona Verma * and R. S. Chandel † * Technocrats Institute of Technology, Bhopal, India. † Govt. Geetanjali College, Bhopal, India. (Received: 5 March 2012, Accepted: 8 May 2012) In this paper, we use the concepts of sub compatibility and sub sequencial continuity in intuitionistic fuzzy metric spaces using implicit relation which are respectively weaker than occasionally weak compatibility and reciprocal continuity. With them, we establish a common fixed point theorem for four maps. Keywords: Intuitionistic fuzzy metric space; Sub compatibility and Sub sequencial continuity; common fixed point theorem; implicit relation. AMS Subject Classification: 47H10, 54H25. 1. Introduction Atanassov [1] introduced and studied the concept of intuitionistic fuzzy sets as a generalization of fuzzy sets [2]. In 2004, Park [3] 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. [4] 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 [5]. Further, Alaca et al. [4] proved Intuitionistic fuzzy Banach and intuitionistic fuzzy Edelstein contraction theorems, with the different definition of Cauchy sequences and completeness than the ones given in [3]. Popa [6, 7] introduced the idea of implicit function to prove a common fixed point theorem in metric spaces Singh and Jain [8] further extended the result of Popa [6, 7] in fuzzy metric spaces. In this paper, we use the concepts of subcompatibility and subsequential continuity in intuitionistic fuzzy metric spaces using implicit relation which are respectively weaker than occasionally weak compatibility and reciprocal continuity. With them, we establish a common fixed point theorem for four maps. 2. Preliminary Notes Definition 2.1 [9] A binary operation * : [0, 1] × [0, 1] → [0, 1] is a continuous t-norms if * is satisfying conditions: (1) * is a commutative and associative; * Corresponding author Email: monaverma117@gmail.com