Viscosity approximations methods for \((\psi,\varphi)\) -weakly contractive mappings

In this paper, we study viscosity approximations with \((\psi,\varphi)\)-weakly contractive mappings. We show that Moudafi’s viscosity approximations follow from Browder and Halpern type convergence theorems. Our results generalize a number of convergence theorems including a strong convergence theorem of Song and Liu (Fixed Point Theory Appl. 2009:824374, 2009).