ITERATION METHOD TO CONSTRUCT FIXED POINT OF NONLINEAR MAPPINGS
构造非线性映射不动点的迭代法

In this paper, we consider the iteration scheme defined by Ishikawa and Mann.It is shown that these iterative schemes converge to the unique fixed point ofgeneralized quasicontractive mapping and to the unique fixed point of Ciric's quasi-contractive mapping. Then we answer positively the open problem mentioned byRhoades. In the next place, we prove the convergence of these iterative processes for thefixed point of generalized nonexpansive mapping and quasi-nonexpansive mapping aswell.