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

Kriengsak Wattanawitoon, Yaowalux Khamlae

Abstract

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.