Convergence theorems and stability results of pointwise asymptotically nonexpansive mapping in Banach space

The purpose of this paper is to approximate the fixed point of pointwise asymptotically nonexpansive mapping using the generalized Mann and generalized Ishikawa iterative scheme. And under the condition that the pointwise asymptotically nonexpansive mapping is compact, the stability results of the two iterative schemes are studied. The main results of this paper modify and improve many important recent results in the literature.