Some Fixed Point Results for Commuting Families of Mappings in Modular Spaces. (3rd October 2021)

• Record Type: Journal Article
• Authors: Domínguez Benavides, T.; Lorenzo Ramírez, P.
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 13(2021)
• Page Start: 1608
• Page End: 1625
• Publication Date: 2021-10-03
• Subjects: Asymptotically nonexpansive mapping -- fixed point -- modular vector space -- measure of noncompactness -- nonexpansive mapping; Primary 47H10 -- 47H04 -- Secondary 46E30; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.2001825
• Languages: English
• ISSNs: 0163-0563

Abstract

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.