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

Abstract In this paper, we study viscosity approximations with $(\psi,\varphi)$ ( ψ , φ ) -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).