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

Authors
Publisher
International Journal of Mathematics and Mathematical Sciences
Publication Date
Disciplines
  • Mathematics

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 {Pu(t):t∈G} exists.

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