Abstract
Recently, Jleli and Samet [Fixed Point Theory Appl. 2016 (2016), doi:10.1186/s13663-016-0504-910.1186/s13663-016-0504-9" TargetType="DOI] established an existence result for the following problem: Find such that , , where (X, d) is a metric space equipped with the two partial orders and , and are given mappings. This existence result was obtained under a continuity assumption imposed on the mappings A, B, C and D. In this paper, we prove that the result of Jleli and Samet holds true by supposing that only A and B are continuous (or only C and D are continuous). Moreover, we prove that the considered problem has one and only one solution. We provide an example to show that our result is a significant generalization of that of Jleli and Samet. Moreover, we consider a more large class of mappings satisfying a certain implicit contraction.