Abstract
Let C be rho-bounded, rho-closed, convex subset of a modular function space L-rho. We investigate the existence of common fixed points for asymptotic pointwise nonexpansive semigroups of nonlinear mappings T-t : C -> C, i.e. a family such that T-o(f) = f, Ts+t(f) = T-s o T-t(f) and
rho(T(f) -T(g)) <= alpha(t)(f)rho(f - g),
where lim sup(t ->infinity) alpha(t)(f) <= 1 for every f is an element of C. In particular, we prove that if L-rho is uniformly convex, then the common fixed point is nonempty rho-closed and convex.