Let C be a ρ-bounded, ρ-closed, convex subset of a modular function space L ρ . 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 0 ( f ) = f , T s + t ( f ) = T s ° T t ( f ) and ρ ( T ( f ) ? T ( g ) ) ≤ α t ( f ) ρ ( f ? g ) , where lim?sup t → ∞ α t ( f ) ≤ 1 for every f ∈ C . In particular, we prove that if L ρ is uniformly convex, then the common fixed point is nonempty ρ-closed and convex. MSC:47H09, 46B20, 47H10, 47E10.
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