Farthest Points and Subdifferential in 𝑝-Normed Spaces
We study the farthest point mapping in a 𝑝-normed space 𝑋 in virtue of subdifferential of 𝑟(𝑥)=sup{‖𝑥−𝑧‖𝑝∶𝑧∈𝑀}, where 𝑀 is a weakly sequentially compact subset of 𝑋. We show that the set of all points in 𝑋 which have farthest point in 𝑀 contains a dense 𝐺𝛿 subset of 𝑋....
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2008/196326 |
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| author | S. Hejazian A. Niknam S. Shadkam |
| author_facet | S. Hejazian A. Niknam S. Shadkam |
| author_sort | S. Hejazian |
| collection | DOAJ |
| description | We study the farthest point mapping in a 𝑝-normed space 𝑋 in virtue of subdifferential
of 𝑟(𝑥)=sup{‖𝑥−𝑧‖𝑝∶𝑧∈𝑀}, where 𝑀 is a weakly sequentially compact
subset of 𝑋. We show that the set of all points in 𝑋 which have farthest point in 𝑀 contains
a dense 𝐺𝛿 subset of 𝑋. |
| format | Article |
| id | doaj-art-52f0b1fd3a354c3f9be41edb453ba84c |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-52f0b1fd3a354c3f9be41edb453ba84c2025-02-03T01:27:26ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252008-01-01200810.1155/2008/196326196326Farthest Points and Subdifferential in 𝑝-Normed SpacesS. Hejazian0A. Niknam1S. Shadkam2Department of Mathematics and Center of Excellence in Analysis on Algebraic structures, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, IranDepartment of Mathematics and Center of Excellence in Analysis on Algebraic structures, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, IranDepartment of Mathematics and Center of Excellence in Analysis on Algebraic structures, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, IranWe study the farthest point mapping in a 𝑝-normed space 𝑋 in virtue of subdifferential of 𝑟(𝑥)=sup{‖𝑥−𝑧‖𝑝∶𝑧∈𝑀}, where 𝑀 is a weakly sequentially compact subset of 𝑋. We show that the set of all points in 𝑋 which have farthest point in 𝑀 contains a dense 𝐺𝛿 subset of 𝑋.http://dx.doi.org/10.1155/2008/196326 |
| spellingShingle | S. Hejazian A. Niknam S. Shadkam Farthest Points and Subdifferential in 𝑝-Normed Spaces International Journal of Mathematics and Mathematical Sciences |
| title | Farthest Points and Subdifferential in
𝑝-Normed Spaces |
| title_full | Farthest Points and Subdifferential in
𝑝-Normed Spaces |
| title_fullStr | Farthest Points and Subdifferential in
𝑝-Normed Spaces |
| title_full_unstemmed | Farthest Points and Subdifferential in
𝑝-Normed Spaces |
| title_short | Farthest Points and Subdifferential in
𝑝-Normed Spaces |
| title_sort | farthest points and subdifferential in 𝑝 normed spaces |
| url | http://dx.doi.org/10.1155/2008/196326 |
| work_keys_str_mv | AT shejazian farthestpointsandsubdifferentialinpnormedspaces AT aniknam farthestpointsandsubdifferentialinpnormedspaces AT sshadkam farthestpointsandsubdifferentialinpnormedspaces |