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Common fixed points for pointwise Lipschitzian semigroups in modular function spaces

Research paper by Buthinah A Bin Dehaish, Mohamed A Khamsi, Wojciech M Kozlowski

Indexed on: 12 Aug '13Published on: 12 Aug '13Published in: Fixed Point Theory and Applications



Abstract

Let C be a ρ-bounded, ρ-closed, convex subset of a modular function space LρOpen image in new window. We investigate the existence of common fixed points for asymptotic pointwise nonexpansive semigroups of nonlinear mappings Tt:C→COpen image in new window, i.e. a family such that T0(f)=fOpen image in new window, Ts+t(f)=Ts∘Tt(f)Open image in new window andwhere lim supt→∞αt(f)≤1Open image in new window for every f∈COpen image in new window. In particular, we prove that if LρOpen image in new window is uniformly convex, then the common fixed point is nonempty ρ-closed and convex.MSC:47H09, 46B20, 47H10, 47E10.