Asymptotic behavior of almost-orbits of reversible semigroups of non-Lipschitzian mappings in Banach spaces. (1997)

• Record Type: Journal Article
• Authors: Jung, Jong Soo; Park, Jong Yeoul; Park, Jong Seo
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 20:Number 1(1997)
• Page Start: 51
• Page End: 60
• Publication Date: 1997
• Subjects: almost-orbit -- fixed point -- reversible semitopological semigroup -- semigroup of asymptotically nonexpansive type -- uniformly convex Banach space; Mathematics -- Periodicals; 510.5
• DOI: 10.1155/S0161171297000094
• Languages: English
• ISSNs: 0161-1712

Abstract

Abstract : LetC be a nonempty closed convex subset of a uniformly convex Banach spaceE with a Fréchet differentiable norm, G a right reversible semitopological semigroup, and𝒮 = { S ( t ) : t ∈ G } a continuous representation ofG as mappings of asymptotically nonexpansive type ofC into itself. The weak convergence of an almost-orbit{ u ( t ) : t ∈ G } of𝒮 = { S ( t ) : t ∈ G } onC is established. Furthermore, it is shown that ifP is the metric projection ofE onto setF ( S ) of all common fixed points of𝒮 = { S ( t ) : t ∈ G }, then the strong limit of the net{ P u ( t ) : t ∈ G } exists.