In the paper,we quote the limit s theory of contractive iterated sequence,which can be used to solve a large number of problems and form a suit of theoretical methods.

Strong convergence of Reich-Takahashi iterative sequence for asymptotically pseudo-contractive mapping;

Strong convergence of some iterative sequences for asymptotically nonexpansive mappings in Banach spances;

Aim\ The convergence of Mann iterative sequences of real functions defined on unbounded convex domain is discussed.

For a lot of nonlinear mappings,the fixed points can be approximated by iteration sequence {xn}.

Convergence of Ishikawa iteration sequence for setvalued nonexpansive mapping are discussed in uniformly covex Banach space, and the conditions are shown which guarantee the convergence of the iteration sequence to a fixed point.

This article will set up an iteration sequence and extent its results to a more comprehensive mapping-semi-compact 1-set mapping.

Some properties of super contraction iteration in 3N+1 conjecture;

In this paper,it is shown that the convergence of Picard iteration sequence is equivalent to Mann iteration sequence,and the convergence of Mann iteration sequence is equivalent to Ishikawa iteration sequence for Zamfirescu operators in an arbitrary Banach space.

In this paper,it is shown that the convergence of Picard iteration sequence is equivalent to Mann iteration sequence,and the convergence of Mann iteration sequence is equivalent to Ishikawa iteration sequence for Zamfirescu operators in an arbitrary Banach space.

Based on Kikkawa and Takahashi iteration method,the Mann iteration sequence is introduced to revise them by using Hybrid projection method.

In the present paper,by virture of the new inequality and the new approximation methods, we prove some new convergence theorems of the Ishikawa and Mann iteration sequences for strongly accretive and strongly pseudo-contractive operators in Banach spaces.