Projection Type Ishikawa Iteration with Perturbations for Common Fixed Points of Two Nonself Generalized Asymptotically Quasi-Nonexpansive Mappings

In this paper, we introduce and study a new type of two-step iterative scheme which is called the projection type Ishikawa iteration with perturbations for two nonself generalized asymptotically quasi-nonexpansive mappings in Banach spaces. A sufficient condition for convergence of the iteration process to a common fixed point of mappings under our setting is also established in a real uniformly convex Banach space. Furthermore, the strong convergence of a new iterative scheme with perturbations to a common fixed point of two nonself generalized asymptotically quasi-nonexpansive mappings on a nonempty closed convex subset of a real Banach space is proved. The results obtained in this paper extend and generalize many important know results in recent literature.