Some Fixed Point Results for Commuting Families of Mappings in Modular Spaces. (3rd October 2021) - Domínguez Benavides, T.; Lorenzo Ramírez, P.
Abstract: Assume that ρ is a convex modular satisfying the Δ 2 -type condition and the modular space is either α -uniformly ρ -noncompact convex or it satisfies the strong Opial condition. We prove that the fixed point set of a commuting family of asymptotically non-expansive mappings defined from a ρ -convex weakly compact set C into C is a non-empty nonexpansive retract of C . We show that our results about existence of fixed point for commuting families of nonexpansive mappings also work if we replace the weak topology by some other topologies weaker than the ρ -topology. In particular, we can obtain fixed point results when C is ρ -a.e. compact in a modular function space.