One-dimensional mean value methods in iterations

A widely used approach for solving problems consists of recasting them as fixed point problems and then using one-dimensional mean value iterative methods. Such methods are therefore of more than passing interest and deserve to be studied for themselves. The representative member of a class of one-dimensional mean value iterative methods, i.e., its representative algorithm schema, uses a convex and closed subset T of En, a continuous map a(??) from T into T and an infinite sequence of scalars {??i} with ??i in [0;1] for all i.