Asymptotic behavior of almost-orbits of reversible semigroups of non-Lipschitzian mappings in Banach spaces

Jong Soo Jung, Jong Yeoul Park and Jong Seo Park

International Journal of Mathematics and Mathematical Sciences, 1997, vol. 20, 1-10

Abstract:

Let C be a nonempty closed convex subset of a uniformly convex Banach space E with a Fréchet differentiable norm, G a right reversible semitopological semigroup, and 𝒮 = { S ( t ) : t ∈ G } a continuous representation of G as mappings of asymptotically nonexpansive type of C into itself. The weak convergence of an almost-orbit { u ( t ) : t ∈ G } of 𝒮 = { S ( t ) : t ∈ G } on C is established. Furthermore, it is shown that if P is the metric projection of E onto set F ( S ) of all common fixed points of 𝒮 = { S ( t ) : t ∈ G } , then the strong limit of the net { P u ( t ) : t ∈ G } exists.

Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:236892

DOI: 10.1155/S0161171297000094

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