Moudafi's viscosity approximations with Meir–Keeler contractions

In this paper, we discuss Moudafi's viscosity approximations with Meir–Keeler contractions. We first present very simple proofs of Xu's theorems concerning Moudafi's approximations. We next prove that Browder's and Halpern's type convergence theorems imply Moudafi's viscosity approximations. Using them, we finally state several deduced theorems.