Asymptotic behavior of almost-orbits of reversible semigroups of non-Lipschitzian mappings in Banach spaces
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 o...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1997-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171297000094 |
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| Summary: | 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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| ISSN: | 0161-1712 1687-0425 |