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

摘要

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 one fixed point, and its Mann iterative sequence converges strongly to the fixed point. Moreover, the estimation between the iterative sequence and the fixed point is, in surface, as the same as in Banach contractive mapping.