On Simultaneous Farthest Points in ๐ฟโ(๐ผ,๐)
Let ๐ be a Banach space and let ๐บ be a closed bounded subset of ๐. For (๐ฅ1,๐ฅ2,โฆ,๐ฅ๐)โ๐๐, we setโโ๐(๐ฅ1,๐ฅ2,โฆ,๐ฅ๐,๐บ)=sup{max1โค๐โค๐โ๐ฅ๐โ๐ฆโโถ๐ฆโ๐บ}. The set ๐บ is called simultaneously remotal if, for any (๐ฅ1,๐ฅ2,โฆ,๐ฅ๐)โ๐๐, there exists ๐โ๐บ such thatโโ๐(๐ฅ1,๐ฅ2,โฆ,๐ฅ๐,๐บ)=max1โค๐โค๐โ๐ฅ๐โ๐โ. In this paper, we show that if...
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2011-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2011/890598 |
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| author | Sh. Al-Sharif M. Rawashdeh |
| author_facet | Sh. Al-Sharif M. Rawashdeh |
| author_sort | Sh. Al-Sharif |
| collection | DOAJ |
| description | Let ๐ be a Banach space and let ๐บ be a closed bounded subset of ๐. For (๐ฅ1,๐ฅ2,โฆ,๐ฅ๐)โ๐๐, we setโโ๐(๐ฅ1,๐ฅ2,โฆ,๐ฅ๐,๐บ)=sup{max1โค๐โค๐โ๐ฅ๐โ๐ฆโโถ๐ฆโ๐บ}. The set ๐บ is called simultaneously remotal if, for any (๐ฅ1,๐ฅ2,โฆ,๐ฅ๐)โ๐๐, there exists ๐โ๐บ such thatโโ๐(๐ฅ1,๐ฅ2,โฆ,๐ฅ๐,๐บ)=max1โค๐โค๐โ๐ฅ๐โ๐โ. In this paper, we show that if ๐บ is separable simultaneously remotal in ๐, then the set of โ-Bochner integrable functions, ๐ฟโ(๐ผ,๐บ), is simultaneously remotal in ๐ฟโ(๐ผ,๐). Some other results are presented. |
| format | Article |
| id | doaj-art-cd230dc403224623b5caef6995ded341 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-cd230dc403224623b5caef6995ded3412025-02-03T05:50:29ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252011-01-01201110.1155/2011/890598890598On Simultaneous Farthest Points in ๐ฟโ(๐ผ,๐)Sh. Al-Sharif0M. Rawashdeh1Mathematics Department, Yarmouk University, Irbid 21163, JordanDepartment of Mathematics and Statistics, Jordan University of Science and Technology, Irbid 22110, JordanLet ๐ be a Banach space and let ๐บ be a closed bounded subset of ๐. For (๐ฅ1,๐ฅ2,โฆ,๐ฅ๐)โ๐๐, we setโโ๐(๐ฅ1,๐ฅ2,โฆ,๐ฅ๐,๐บ)=sup{max1โค๐โค๐โ๐ฅ๐โ๐ฆโโถ๐ฆโ๐บ}. The set ๐บ is called simultaneously remotal if, for any (๐ฅ1,๐ฅ2,โฆ,๐ฅ๐)โ๐๐, there exists ๐โ๐บ such thatโโ๐(๐ฅ1,๐ฅ2,โฆ,๐ฅ๐,๐บ)=max1โค๐โค๐โ๐ฅ๐โ๐โ. In this paper, we show that if ๐บ is separable simultaneously remotal in ๐, then the set of โ-Bochner integrable functions, ๐ฟโ(๐ผ,๐บ), is simultaneously remotal in ๐ฟโ(๐ผ,๐). Some other results are presented.http://dx.doi.org/10.1155/2011/890598 |
| spellingShingle | Sh. Al-Sharif M. Rawashdeh On Simultaneous Farthest Points in ๐ฟโ(๐ผ,๐) International Journal of Mathematics and Mathematical Sciences |
| title | On Simultaneous Farthest Points in ๐ฟโ(๐ผ,๐) |
| title_full | On Simultaneous Farthest Points in ๐ฟโ(๐ผ,๐) |
| title_fullStr | On Simultaneous Farthest Points in ๐ฟโ(๐ผ,๐) |
| title_full_unstemmed | On Simultaneous Farthest Points in ๐ฟโ(๐ผ,๐) |
| title_short | On Simultaneous Farthest Points in ๐ฟโ(๐ผ,๐) |
| title_sort | on simultaneous farthest points in ๐ฟโ ๐ผ ๐ |
| url | http://dx.doi.org/10.1155/2011/890598 |
| work_keys_str_mv | AT shalsharif onsimultaneousfarthestpointsinlix AT mrawashdeh onsimultaneousfarthestpointsinlix |