Common fixed points for pointwise Lipschitzian semigroups in modular function spaces
Buthinah Abdullatif Bin Dehaish, Mohamed A. Khamsi, Wojciech M. Kozƚowski · Fixed Point Theory and Applications · 2013
Let C be a ρ-bounded, ρ-closed, convex subset of a modular function space . We investigate the existence of common fixed points for asymptotic pointwise nonexpansive semigroups of nonlinear mappings , i.e. a family such that , and where for every . In particular, we prove that if is uniformly convex, then the common fixed point is nonempty ρ-closed and convex. MSC:47H09, 46B20, 47H10, 47E10.