On Best Proximity Point Theorems without Ordering
Recently, Basha (2013) addressed a problem that amalgamates approximation and optimization in the setting of a partially ordered set that is endowed with a metric. He assumed that if A and B are nonvoid subsets of a partially ordered set that is equipped with a metric and S is a non-self-mapping fr...
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Hindawi Limited
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/130439 |
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doaj-749ac6b93559415386401081275aad692020-11-24T23:28:17ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/130439130439On Best Proximity Point Theorems without OrderingA. P. Farajzadeh0S. Plubtieng1K. Ungchittrakool2Department of Mathematics, Razi University, Kermanshah 67149, IranDepartment of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, ThailandDepartment of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, ThailandRecently, Basha (2013) addressed a problem that amalgamates approximation and optimization in the setting of a partially ordered set that is endowed with a metric. He assumed that if A and B are nonvoid subsets of a partially ordered set that is equipped with a metric and S is a non-self-mapping from A to B, then the mapping S has an optimal approximate solution, called a best proximity point of the mapping S, to the operator equation Sx=x, when S is a continuous, proximally monotone, ordered proximal contraction. In this note, we are going to obtain his results by omitting ordering, proximal monotonicity, and ordered proximal contraction on S.http://dx.doi.org/10.1155/2014/130439 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
A. P. Farajzadeh S. Plubtieng K. Ungchittrakool |
| spellingShingle |
A. P. Farajzadeh S. Plubtieng K. Ungchittrakool On Best Proximity Point Theorems without Ordering Abstract and Applied Analysis |
| author_facet |
A. P. Farajzadeh S. Plubtieng K. Ungchittrakool |
| author_sort |
A. P. Farajzadeh |
| title |
On Best Proximity Point Theorems without Ordering |
| title_short |
On Best Proximity Point Theorems without Ordering |
| title_full |
On Best Proximity Point Theorems without Ordering |
| title_fullStr |
On Best Proximity Point Theorems without Ordering |
| title_full_unstemmed |
On Best Proximity Point Theorems without Ordering |
| title_sort |
on best proximity point theorems without ordering |
| publisher |
Hindawi Limited |
| series |
Abstract and Applied Analysis |
| issn |
1085-3375 1687-0409 |
| publishDate |
2014-01-01 |
| description |
Recently, Basha (2013) addressed a problem that amalgamates approximation and optimization in the setting of a partially ordered set that is endowed with a metric. He assumed that if A and B are nonvoid subsets of a partially ordered set that is equipped with a metric and S is a non-self-mapping from A to B, then the mapping S has an optimal approximate solution, called a best proximity point of the mapping S, to the operator equation Sx=x, when S is a continuous, proximally monotone, ordered proximal contraction. In this note, we are going to obtain his results by omitting ordering, proximal monotonicity, and ordered proximal contraction on S. |
| url |
http://dx.doi.org/10.1155/2014/130439 |
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AT apfarajzadeh onbestproximitypointtheoremswithoutordering AT splubtieng onbestproximitypointtheoremswithoutordering AT kungchittrakool onbestproximitypointtheoremswithoutordering |
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