Convergence to common fixed points by a modified iteration process

Abstract

We modify an iteration process of Agarwal et al. (J. Nonlinear Convex Anal. 8(1):61–79, 2007) to the case of two mappings and prove some weak and strong convergence theorems for two asymptotically nonexpansive mappings. We also point out that this process cannot be used for three mappings in its existing form even for nonexpansive mappings. We have to impose an extra condition to get convergence. We give an example to show that there do exist two nonexpansive mappings satisfying that condition.