ISSN(Online): 2319-8753 ISSN (Print): 2347-6710 International Journal of Innovative Research in Science, Engineering and Technology (An I SO 3297: 2007 Certified Organization) Vol. 5, Issue 6, June 2016 Copyright to IJIRSET DOI:10.15680/IJIRSET.2015.0506175 10465 Six Maps with a Common Fixed Point Satisfying Weak Compatible and Commuting Mapping in complex valued metric space Using Rational Inequalities Kamal Kumar 1 , Nisha Sharma 2,* , Rajeev Jha 3 , Ritu Sharma 4 , Sheetal Sharma 5 Department of Mathematics, Pt. JLN Govt. College Faridabad, Sunrise University Alwar, India 1 Department of Mathematics, Pt. JLN Govt. College Faridabad, Faridabad, Haryana, India 2 Department of Mathematics, Teerthankar Mahaveer University, Moradabad, U.P, India 3 Department of Mathematics, Pt. JLN Govt. College Faridabad, India 4 Assistant Professor, Department of computer Science and Engineering, Amity university sector-125, Noida, India 5 * Corresponding Author ABSTRACT. Azam et al. (2011), introduce the notion of complex valued metric spaces and obtained common fixed point result for mappings in the context of complex valued metric spaces. In this paper we prove common fixed point theorems for six maps in complex valued metric space satisfying commuting and weakly compatible mappingwith different type of inequality,our result generalizes the result of Tiwari et al.[8] KEYWORDS: commuting mapping, weakly compatible maps, common fixed points, complete complex valued metric space MSC: 46T99, 47H10, 54H25, 54C30 I. INTRODUCTION Banach contraction principle was the starting point for many researchers during last few decades in the field of nonlinear analysis. The concept of complex valued metric pace which is a generalization of the classical metric space was recently introduced by Azam, Fisher and khan[1]. The study of metric space expressed the most common important role to many fields both in pure and applied science [3]. Abounding researchers extended the notion of a metric space such as vector valued metric space of Perov [2], a cone metric spaces of Huang and Zhang [6], a modular metric spaces of Chistyakov[10], etc. For the sake of completeness we recollect some basic definitions and fundamentals results on the topic in the literature. We mainly follow the notions and notations of Azam et al.[1]. Let ℂ be the set of all complex numbers,for z 1 ,z 2 ∈ℂ, define a partial order ≾ on ℂ as follows; z 1 ≾z 2 iff Re(z 1 ) ≤ Re(z 2 ), Im(z 1 ) ≤ Im(z 2 ) it follows that z 1 ≾z 2 , if one of the following conditions is satisfied: i. Re(z 1 )= Re(z 2 ), Im(z 1 )< Im(z 2 )