Abstract
Let
{(X,\lVert\,\cdot\,\rVert)}
be a Banach space. Let C be a nonempty,
bounded, closed and convex subset of X and let
{T:C\rightarrow C}
be a G-monotone nonexpansive mapping. In this work, it is shown
that the Mann iteration sequence defined by
x_{n+1}=t_{n}T(x_{n})+(1-t_{n})x_{n},\quad n=1,2,\dots,
proves the existence of a fixed point of G-monotone nonexpansive
mappings.