Available online at www.isr-publications.com/jmcs J. Math. Computer Sci., 18 (2018), 216–231 Research Article Journal Homepage: www.tjmcs.com - www.isr-publications.com/jmcs Common fixed point theorems for two pairs of self-mappings in partial metric space using C-class functions on (ψ, ϕ)-contractive condition Zead Mustafa a,b,* , M. M. M. Jaradat a , Arslan Ansari c , Feng Gu d , Hui-hui Zheng d , Stojan Radenovi´ c e , M. S. Bataineh f a Department of Mathematics, Statistics and Physics, Qatar University, Doha-Qatar. b Department of Mathematics, The Hashemite University, Zarqa 13133, Jordan. c Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran. d Institute of Applied Mathematics and Department of Mathematics, Hangzhou Normal University, Hangzhou, Zhejiang 310036, China. e Faculty of Mechanical Engineering, University of Belgrade, Serbia. f Department of Mathematics, University of Sharjah, Sharjah, United Arab Emirates. Abstract The purpose of this paper is to introduce common fixed point results for two pairs of weakly compatible self-mappings in partial metric space using C-class functions on (ψ, ϕ)-contractive condition. Example and application on integral equations are presented to illustrate the main result. Our results extend and generalize well know results in the literature. Keywords: (ψ, ϕ)-Contractive mapping, common fixed point, coincidence point, partial metric space, weakly compatible mappings, C-class functions, integral equations. 2010 MSC: 47H10, 54H25. c 2018 All rights reserved. 1. Introduction and mathematical preliminaries In 1994, Matthews [17] introduced the notion of partial metric spaces and obtained various fixed point theorems. In fact, he showed that the Banach contraction mapping theorem can be generalized to the partial metric context. Later on, Romaguera [30] introduced the notions of 0-Cauchy sequences and 0-complete partial met- ric spaces and proved some characterizations of partial metric spaces in terms of completeness and 0- completeness. Afterwards, several authors obtained some fixed point results for mappings satisfying * Corresponding author Email addresses: zead@qu.edu.qa (Zead Mustafa), mmjst4@qu.edu.qa (M. M. M. Jaradat), analsisamirmath2@gmail.com (Arslan Ansari), gufeng_99@163.com (Feng Gu), zhenghuihui910@sina.com (Hui-hui Zheng), radens@beotel.net (Stojan Radenovi´ c), bataineh71@hotmail.com (M. S. Bataineh) doi: 10.22436/jmcs.018.02.09 Received 2017-03-01