Next, some Mann type iterative ap-proximation sequences with errors for these nonoscillatory solutionsare constructed and the error estimates between the approximate so-lutions and the nonoscillatory solutions are also discussed.

On the Mann-type iteration method for solutions to varational inclusion problems with strongly accretive-type mappings;

Suppose that {an} is chosen in such a way that δ≤an≤1-δ for all n,where δ∈(0,1) is a small enough constant,then for arbitrary x0∈K,the sequence {xn} given by the Mann type implicit iteration process xn=anxn-1+(1-an)Tnxn(n>0) weakly converges to the fixed point of T.

Furthermore the author considers a new class of generalized variational inclusions involving A-accretive operator and proposes a Mann-type iterative algorithm for approximating the solution of this class of generalized variational inclusions by using the resolvent operator technique for A-accretive operator.

The convergence of Mann iterative sequences of solutions for some mixed monotone operator equations;

The convergence of Mann iterative sequences of solutions for some nonlinear operator equations

The existence and uniqueness of random fixed point of random non-monotone binary operator equations without compactness conditions was studied by using the cone theory and Mann iterative technique,and the iteration sequences which converge to solution of operator equations and the error estimates were also given.

Mann Iteration Process for Certain Nonlinear Mappings in q -uniformaly Smooth Banach Spaces;

In quniformly smooth Banach,it is investigated that the convergence of Mann iteration for generalized Lipschitzian Φ pseudo contractive and accretive mappings,which improves and extends corresponding present results.

In this paper,we establish the equivalence between the convergence of Mann iteration with errors with the convergence of Ishikawa iteration with errors,where T is an uniformly continuous strongly pseudo-contractive mapping.