We introduce a kind of new hybrid projection algorithm for quasi-φ-asymptotically nonexpansive mappings in reflexive,strictly convex and smooth Banach spaces,and establish a new strong convergence theorem by using new analysis techniques,which improves and extends recent some relative results.

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.

Weak congervence to fixed points of asymptotically nonexpansive mappings by modified Ishikawa iterative sequence;

This paper investigates into the fixed points for asymptotically nonexpansive mappings in uniformly convex Banach X spaces.

This paper attempts to study the stability problem of asymptotically nonexpansive mapping in Banach space, and does not require the boundedness of domain and range; moreover,useing a new method to be a proof that it is true.

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.

Based on Mann iteration method, the sequence of asymptotically nonexpansive mapping generated by iteration is located in a closed and convex set by using the generalized projection.

Without making the usual basic assumption that:∑∞n=1(k_n-1)<∞ or∑∞n=1(k~p_n-1)<∞,fixed point iterative construction problem is studied for a class of concrete asymptotically nonexpansive mappings,and several strong convergence results are obtained,where p>1 is fixed real number and ｛k_n｝ is the asymptotic sequence of asymptotically nonexpansive mappings under considered.