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Fixed point iteration processes for asymptotic pointwise nonexpansive mapping in modular function spaces

Research paper by Buthinah A Bin Dehaish, WM Kozlowski

Indexed on: 20 Jul '12Published on: 20 Jul '12Published in: Fixed Point Theory and Applications



Abstract

Let LρOpen image in new window be a uniformly convex modular function space with a strong Opial property. Let T:C→COpen image in new window be an asymptotic pointwise nonexpansive mapping, where C is a ρ-a.e. compact convex subset of LρOpen image in new window. 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.