Invariant Means and Reversible Semigroup of Relatively Nonexpansive Mappings in Banach Spaces
The purpose of this paper is to study modified Halpern type and Ishikawa type iteration for a semigroup of relatively nonexpansive mappings I={T(s):s∈S} on a nonempty closed convex subset C of a Banach space with respect to a sequence of asymptotically left invariant means {μn} defined on an appropr...
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Hindawi Limited
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/694783 |
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doaj-a03fb64c0b6d466789dd9a3332d11cce2020-11-24T23:39:15ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/694783694783Invariant Means and Reversible Semigroup of Relatively Nonexpansive Mappings in Banach SpacesKyung Soo Kim0Graduate School of Education, Mathematics Education, Kyungnam University, Changwon 631-701, Republic of KoreaThe purpose of this paper is to study modified Halpern type and Ishikawa type iteration for a semigroup of relatively nonexpansive mappings I={T(s):s∈S} on a nonempty closed convex subset C of a Banach space with respect to a sequence of asymptotically left invariant means {μn} defined on an appropriate invariant subspace of l∞(S), where S is a semigroup. We prove that, given some mild conditions, we can generate iterative sequences which converge strongly to a common element of the set of fixed points F(I), where F(I)=⋂{F(T(s)):s∈S}.http://dx.doi.org/10.1155/2014/694783 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Kyung Soo Kim |
| spellingShingle |
Kyung Soo Kim Invariant Means and Reversible Semigroup of Relatively Nonexpansive Mappings in Banach Spaces Abstract and Applied Analysis |
| author_facet |
Kyung Soo Kim |
| author_sort |
Kyung Soo Kim |
| title |
Invariant Means and Reversible Semigroup of Relatively Nonexpansive Mappings in Banach Spaces |
| title_short |
Invariant Means and Reversible Semigroup of Relatively Nonexpansive Mappings in Banach Spaces |
| title_full |
Invariant Means and Reversible Semigroup of Relatively Nonexpansive Mappings in Banach Spaces |
| title_fullStr |
Invariant Means and Reversible Semigroup of Relatively Nonexpansive Mappings in Banach Spaces |
| title_full_unstemmed |
Invariant Means and Reversible Semigroup of Relatively Nonexpansive Mappings in Banach Spaces |
| title_sort |
invariant means and reversible semigroup of relatively nonexpansive mappings in banach spaces |
| publisher |
Hindawi Limited |
| series |
Abstract and Applied Analysis |
| issn |
1085-3375 1687-0409 |
| publishDate |
2014-01-01 |
| description |
The purpose of this paper is to study modified Halpern type and Ishikawa type iteration for a semigroup of relatively nonexpansive mappings I={T(s):s∈S} on a nonempty closed convex subset C of a Banach space with respect to a sequence of asymptotically left invariant means {μn} defined on an appropriate invariant subspace of l∞(S), where S is a semigroup. We prove that, given some mild conditions, we can generate iterative sequences which converge strongly to a common element of the set of fixed points F(I), where F(I)=⋂{F(T(s)):s∈S}. |
| url |
http://dx.doi.org/10.1155/2014/694783 |
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AT kyungsookim invariantmeansandreversiblesemigroupofrelativelynonexpansivemappingsinbanachspaces |
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