Weak and Strong Convergence Theorems for an alpha-Nonexpansive Mapping and a Generalized Nonexpansive Mapping in Hilbert Spaces

In this paper, we investigate iterative scheme for approximating common solution of fixed point problems involving an alpha-nonexpansive mapping and a generalized nonexpansive mapping in the framework of Hilbert spaces via Takahashi and Tamura's scheme. We obtain the weak convergence theorem under appropriate conditions and strong convergence theorem by adding some necessary condition in the same scheme. Our results extend and improve some recent results in the literature.