Strong Convergence Theorems for Common Fixed Points of an Infinite Family of Asymptotically Nonexpansive Mappings

Abstract

In the framework of a real Banach space with uniformly Gateaux differentiable norm, some new viscosity iterative sequences $\{x_n\}$ are introduced for an infinite family of asymptotically nonexpansive mappings ${\left\{T_i\right\}}_{i=1}^{\infty }$ in this paper. Under some appropriate conditions, we prove that the iterative sequences $\{x_n\}$ converge strongly to a common fixed point of the mappings ${\left\{T_i\right\}}_{i=1}^{\infty }$, which is also a solution of a variational inequality. Our results extend and improve some recent results of other authors.