## Some control conditions on iterative methods.(English)Zbl 1088.47053

The authors obtain some control conditions on iterative methods and prove some strong convergence theorems of iterative sequences for nonexpansive mappings in uniformly smooth Banach spaces. The results presented in this paper unify and improve several known results.

### MSC:

 47J25 Iterative procedures involving nonlinear operators 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 65J15 Numerical solutions to equations with nonlinear operators