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

Abstract EN

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 T i i = 1 ∞ 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 T i i = 1 ∞ , which is also a solution of a variational inequality.

Our results extend and improve some recent results of other authors.