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 arbitrary Banach spaces,it is shown that the convergence of Mann iteration is equivalent to Noor iteration sequence,and the convergence of Mann iteration is equivalent to Ishikawa iteration sequence for generalized-contractive mappings.

Convergence of Ishikawa iterative sequences in uniformly convex Banach spaces;

It proves in a Banach space that Ishikawa iterative sequence strongly converges at the fixed point of strictly pseudocontractive mappings on arbitrary closed, convex sets.

Let T:K→K be a uniformly continuous φ_hemicontractive mapping with bounded codomain range,then the Ishikawa iterative sequence converges strongly to the unique fixed point of T .

We abtain the strong convergence theorem for Ishikawa iterative sequence of Lipschitz φ- strongly accretive operator.

In convex metric spaces,we have proved that if C is a nonempty closed convex,the mapping T in some conditions will have a fixed point and Ishikawa iteration {xn} will converge to the fixed point of T.

Some equivalent conditions are obtained for the convergence of Mann teration,Ishikawa iteration with mixed errors and mann iteration with mixed errors for Lipschitz strongly pseudo-contractive mappings in Banach spaces.

We construct a new Ishikawa iteration process and prove approximating fixed point of asymptotically (?)-pseudocontractive mapping by using that processes.

The problems on convergence of fixed point with Ishikawa iterative process for quasi-contractive mapping pair and generalized contractive mapping in Banach spaces are studied.