Fixed Point Theorems for an Elastic Nonlinear Mapping in Banach Spaces
Let E be a smooth Banach space with a norm ·. Let V(x,y)=x2+y2-2 x,Jy for any x,y∈E, where ·,· stands for the duality pair and J is the normalized duality mapping. We define a V-strongly nonexpansive mapping by V(·,·). This nonlinear mapping is nonexpansive in a Hilbert space. However, we show that...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2015/760671 |
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| author | Hiroko Manaka |
| author_facet | Hiroko Manaka |
| author_sort | Hiroko Manaka |
| collection | DOAJ |
| description | Let E be a smooth Banach space with a norm ·. Let V(x,y)=x2+y2-2 x,Jy for any x,y∈E, where ·,· stands for the duality pair and J is the normalized duality mapping. We define a V-strongly nonexpansive mapping by V(·,·). This nonlinear mapping is nonexpansive in a Hilbert space. However, we show that there exists a V-strongly nonexpansive mapping with fixed points which is not nonexpansive in a Banach space. In this paper, we show a weak convergence theorem and strong convergence theorems for fixed points of this elastic nonlinear mapping and give the existence theorem. |
| format | Article |
| id | doaj-art-f157823c164d47ef9143846e61a4b84d |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-f157823c164d47ef9143846e61a4b84d2025-02-03T06:06:14ZengWileyAbstract and Applied Analysis1085-33751687-04092015-01-01201510.1155/2015/760671760671Fixed Point Theorems for an Elastic Nonlinear Mapping in Banach SpacesHiroko Manaka0Department of Mathematics, Graduate School of Environment and Information Sciences, Yokohama National University, Tokiwadai, Hodogayaku, Yokohama 240-8501, JapanLet E be a smooth Banach space with a norm ·. Let V(x,y)=x2+y2-2 x,Jy for any x,y∈E, where ·,· stands for the duality pair and J is the normalized duality mapping. We define a V-strongly nonexpansive mapping by V(·,·). This nonlinear mapping is nonexpansive in a Hilbert space. However, we show that there exists a V-strongly nonexpansive mapping with fixed points which is not nonexpansive in a Banach space. In this paper, we show a weak convergence theorem and strong convergence theorems for fixed points of this elastic nonlinear mapping and give the existence theorem.http://dx.doi.org/10.1155/2015/760671 |
| spellingShingle | Hiroko Manaka Fixed Point Theorems for an Elastic Nonlinear Mapping in Banach Spaces Abstract and Applied Analysis |
| title | Fixed Point Theorems for an Elastic Nonlinear Mapping in Banach Spaces |
| title_full | Fixed Point Theorems for an Elastic Nonlinear Mapping in Banach Spaces |
| title_fullStr | Fixed Point Theorems for an Elastic Nonlinear Mapping in Banach Spaces |
| title_full_unstemmed | Fixed Point Theorems for an Elastic Nonlinear Mapping in Banach Spaces |
| title_short | Fixed Point Theorems for an Elastic Nonlinear Mapping in Banach Spaces |
| title_sort | fixed point theorems for an elastic nonlinear mapping in banach spaces |
| url | http://dx.doi.org/10.1155/2015/760671 |
| work_keys_str_mv | AT hirokomanaka fixedpointtheoremsforanelasticnonlinearmappinginbanachspaces |