Unified implicit common fixed point theorems under non-negative complex valued functions satisfying the identity of indiscernible


Deepak Singh - Department of Applied Sciences, NITTTR, Under Ministry of HRD, Govt. of India, Bhopal, (M.P.) 462002, India. Vishal Joshi - Department of Applied Mathematics, Jabalpur Engineering College, Jabalpur, (M.P.), India. Mohammad Imdad - Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India. Poom Kumam - Department of Mathematics & Theoretical and Computational Science (TaCS) Center, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand. - China Medical University, No. 91, Hsueh-Shih Road, Taichung, Taiwan.


In this paper, we consider a non-negative complex valued function satisfying the identity of indiscernible and utilize the same to prove some common fixed point theorems for two pairs of non-vacuously weakly compatible mappings satisfying an implicit relation having rational terms as its co-ordinates. Some illustrative examples are also given which demonstrate the validity of the hypotheses of our results. In process, a host of previously known results in the context of complex as well as real valued metric spaces are generalized and improved.