Fixed-Point Existence and Approximation Theorem for Controllable Mapping with Mann Iterative Procedure

The concept of controllable mapping,which is a kind of Lipschitzian mapping,is induced.In certain case,any controllable mapping,on a closed convex subset of Banach space,has at least onefixed point,and its Mann iterative sequence converges strongly to the fixed point.Moreover,theestimation between the iterative sequence and the fixed point is,in sulface,as the same as in Banachcontractive mapping.