On common approximate fixed points of monotone nonexpansive semigroups in Banach spaces.

In this paper, we investigate the common approximate fixed points of monotone nonexpansive semigroups of nonlinear mappings $\{T(t)\}_{t \geq0}$, i.e., a family such that $T(0)x=x$, $T(s+t)x=T(s)\circ T(t)x $, where the domain is a Banach space. In particular we prove that under suitable conditions, the common approximate fixed points are the same as the common approximate fixed points set of two mappings from the family. Then we give an algorithm of how to construct an approximate fixed point sequence of the semigroup in the case of a uniformly convex Banach space. [ABSTRACT FROM AUTHOR]