Journal of Advances in Mathematics and Computer Science 35(4): 87-105, 2020; Article no.JAMCS.57970 ISSN: 2456-9968 (Past name: British Journal of Mathematics & Computer Science, Past ISSN: 2231-0851) _____________________________________ *Corresponding author: E-mail: anilbakhru@gmail.com; A New Common Fixed-Point Theorem for Two Pairs of Mappings in Parametric Metric Space Anil Bakhru 1* , Manoj Ughade 2 and Richa Gupta 3 1 Department of Mathematics, Sardar Vallabhbhai Polytechnic College, College of University of Technology of Madhya Pradesh, Bhopal, 462002, India. 2 Department of Post Graduate Studies and Research in Mathematics, Jaywanti Haksar Government Post Graduate College, College of Chhindawara University, Betul, 460001, India. 3 Department of Engineering Mathematics and Research Center, Sarvepalli Radhakrishanan University, Bhopal, 462026, India. Authors’ contributions All authors contributed equally and significantly to writing this paper. All authors read and approved the final manuscript. Article Information DOI: 10.9734/JAMCS/2020/v35i430273 Editor(s): (1) Dr. Serkan Araci, Hasan Kalyoncu University, Turkey. Reviewers: (1) Narayan Prasad Pahari, Tribhuvan University, Nepal. (2) B. Y. Aiyetan, University of Ilorin, Nigeria. Complete Peer review History: http://www.sdiarticle4.com/review-history/57970 Received: 14 April 2020 Accepted: 19 June 2020 Published: 04 July 2020 _______________________________________________________________________________ Abstract Our aim of this paper is to prove a new general common fixed point theorem for two pair of mappings under a different set of conditions using the idea of weakly compatible mappings satisfying a general class of contractions defined by an implicit relation in the frame work of parametric metric space, which unify, extend and generalize most of the existing relevant common fixed point theorems from the literature. Some related results and illustrative an example to highlight the realized improvements is also furnished. Keywords: Parametric metric space; common fixed point; implicit relation; weakly compatible mappings; contractions. 1 Introduction and Preliminaries Fixed point theory has attracted many researchers since 1922 with the admired Banach fixed point theorem (see [1]). Banach’s contraction principle is one of the pivotal results of analysis. Its significance lies in its Original Research Article