On the convergence of iteration processes for semigroups of nonlinear mappings in modular function spaces

Let C be a ρ-bounded, ρ-closed, convex subset of a modular function space Lρ. We investigate the problem of constructing common fixed points for asymptotic pointwise nonexpansive semigroups of mappings Tt : C → C, i.e. a family such that T0(f) = f, Ts+t(f) = Ts ◦ Tt(f), and ρ(T(f) – T(g)) ≤ αt(f)ρ(f – g), where lim supt→∞ αt(f) ≤ 1, for every f ∈ C