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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| Format: | Article |
| Language: | English |
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Wiley
1997-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171297000094 |
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| _version_ | 1849683959574691840 |
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| author | Jong Soo Jung Jong Yeoul Park Jong Seo Park |
| author_facet | Jong Soo Jung Jong Yeoul Park Jong Seo Park |
| author_sort | Jong Soo Jung |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-cb6299cf8f874ae8920c40d4becd8952 |
| institution | DOAJ |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1997-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-cb6299cf8f874ae8920c40d4becd89522025-08-20T03:23:37ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251997-01-01201516010.1155/S0161171297000094Asymptotic behavior of almost-orbits of reversible semigroups of non-Lipschitzian mappings in Banach spacesJong Soo Jung0Jong Yeoul Park1Jong Seo Park2Department of Mathematics, Dong-A University, Pusan 607-714, KoreaDepartment of Mathematics, Pusan National University, Pusan 609-735, KoreaDepartment of Mathematics, Graduate School, Dong-A University, Pusan 607-714, KoreaLet 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.http://dx.doi.org/10.1155/S0161171297000094almost-orbitfixed pointreversible semitopological semigroup semigroup of asymptotically nonexpansive typeuniformly convex Banach space. |
| spellingShingle | Jong Soo Jung Jong Yeoul Park Jong Seo Park Asymptotic behavior of almost-orbits of reversible semigroups of non-Lipschitzian mappings in Banach spaces International Journal of Mathematics and Mathematical Sciences almost-orbit fixed point reversible semitopological semigroup semigroup of asymptotically nonexpansive type uniformly convex Banach space. |
| title | Asymptotic behavior of almost-orbits of reversible semigroups of non-Lipschitzian mappings in Banach spaces |
| title_full | Asymptotic behavior of almost-orbits of reversible semigroups of non-Lipschitzian mappings in Banach spaces |
| title_fullStr | Asymptotic behavior of almost-orbits of reversible semigroups of non-Lipschitzian mappings in Banach spaces |
| title_full_unstemmed | Asymptotic behavior of almost-orbits of reversible semigroups of non-Lipschitzian mappings in Banach spaces |
| title_short | Asymptotic behavior of almost-orbits of reversible semigroups of non-Lipschitzian mappings in Banach spaces |
| title_sort | asymptotic behavior of almost orbits of reversible semigroups of non lipschitzian mappings in banach spaces |
| topic | almost-orbit fixed point reversible semitopological semigroup semigroup of asymptotically nonexpansive type uniformly convex Banach space. |
| url | http://dx.doi.org/10.1155/S0161171297000094 |
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