Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 13 2 2022 07 01 Common fixed point theorems under implicit contractive condition using E. A. property on metric-like spaces employing an arbitrary binary relation with some application 2325 2346 6645 10.22075/ijnaa.2021.23494.2548 EN Lucas Wangwe Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam, Tanzania Santosh Kumar Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam, Tanzania Journal Article 2021 05 24 In this paper, parallel to the ideas based on Ahmadullah et al. [3, 4, 5], and Eke et al. [17], we prove the existence and uniqueness of the common fixed point for a pair of self-mappings employing (E. A.)-property in metric-like spaces for implicit contractive mappings related to binary relation. Henceforth, results obtained will be verified with the help of illustrative examples. As an application of the results, we solve two boundary value problems of the second-order differential equation. https://ijnaa.semnan.ac.ir/article_6645_c5642e6b31d2dc1cb0a42d1f885227bf.pdf