The author studied the iterative approximation problem of fixed points for asymptotically quasi-nonexpansive type mappings and asymptotically nonexpansive type mappings in Banach spaces under some new condition.

The strong convergence of Ishikawa iterative sequences for asymptotically quasi-nonexpansive type mappings;

In the paper,we obtain some iterative approximation theorems of fixed points for asymptotically quasi-nonexpansive type mapping and asymptotically nonexpansive type mapping with error member in uniformly convex Banach space without the con- dition"for ■ε>0,■n_0∈N_+,■n≥n_0 and ■x∈D,suth that‖T~nx-T~(n+1)x‖<ε.

This paper studied the iterative approximation problem of fixed points for asymptotically quasi-nonexpansive type mappings with mixed errors in uniformly convex Banach space.

This paper introduces N-step iterative sequence with mixed errors and gives a necessary and sufficient condition for the N-step iterative sequence with mixed errors to converges strongly to a common fixed point of a finite family of generalized asymptotically quasi-nonexpansive type mappings in a general Banach space.

Implicit iterative approximation for a finite family of asymptotically nonexpansive mappings in Banach spaces;

In the present paper, several strong convergence results for the modified multistep iterative schemes for a class of asymptotically nonexpansive mappings were established.