Abstract
Let Lρ be a uniformly convex modular function space with a strong Opial property. Let T:C→C be an asymptotic pointwise nonexpansive mapping, where C is a ρ-a.e. compact convex subset of Lρ. In this paper, we prove that the generalized Mann and Ishikawa processes converge almost everywhere to a fixed point of T. In addition, we prove that if C is compact in the strong sense, then both processes converge strongly to a fixed point.MSC:
47H09, 47H10.