More on reverse triangle inequality in inner product spaces
Refining some results of Dragomir, several new reverses of the generalized triangle inequality in inner product spaces are given. Among several results, we establish some reverses for the Schwarz inequality. In particular, it is proved that if a is a unit vector in a real or complex inner product sp...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2005-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.2883 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832567254877732864 |
|---|---|
| author | A. H. Ansari M. S. Moslehian |
| author_facet | A. H. Ansari M. S. Moslehian |
| author_sort | A. H. Ansari |
| collection | DOAJ |
| description | Refining some results of Dragomir, several new reverses of the generalized triangle inequality in inner product spaces are given. Among several results, we establish some reverses for the Schwarz inequality. In particular, it is proved that if a is a unit vector in a real or complex inner product space (H;〈.,.〉), r,s>0, p∈(0,s], D={x∈H,‖rx−sa‖≤p}, x1,x2∈D−{0}, and αr,s=min{(r2‖xk‖2−p2+s2)/2rs‖xk‖:1≤k≤2}, then (‖x1‖‖x2‖−Re〈x1,x2〉)/(‖x1‖+‖x2‖)2≤αr,s. |
| format | Article |
| id | doaj-art-b2672318d69447c38cc3c0ba525d188f |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-b2672318d69447c38cc3c0ba525d188f2025-02-03T01:01:59ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-012005182883289310.1155/IJMMS.2005.2883More on reverse triangle inequality in inner product spacesA. H. Ansari0M. S. Moslehian1Department of Mathematics, Ferdowsi University, P.O. Box 1159, Mashhad 91775, IranDepartment of Mathematics, Ferdowsi University, P.O. Box 1159, Mashhad 91775, IranRefining some results of Dragomir, several new reverses of the generalized triangle inequality in inner product spaces are given. Among several results, we establish some reverses for the Schwarz inequality. In particular, it is proved that if a is a unit vector in a real or complex inner product space (H;〈.,.〉), r,s>0, p∈(0,s], D={x∈H,‖rx−sa‖≤p}, x1,x2∈D−{0}, and αr,s=min{(r2‖xk‖2−p2+s2)/2rs‖xk‖:1≤k≤2}, then (‖x1‖‖x2‖−Re〈x1,x2〉)/(‖x1‖+‖x2‖)2≤αr,s.http://dx.doi.org/10.1155/IJMMS.2005.2883 |
| spellingShingle | A. H. Ansari M. S. Moslehian More on reverse triangle inequality in inner product spaces International Journal of Mathematics and Mathematical Sciences |
| title | More on reverse triangle inequality in inner product spaces |
| title_full | More on reverse triangle inequality in inner product spaces |
| title_fullStr | More on reverse triangle inequality in inner product spaces |
| title_full_unstemmed | More on reverse triangle inequality in inner product spaces |
| title_short | More on reverse triangle inequality in inner product spaces |
| title_sort | more on reverse triangle inequality in inner product spaces |
| url | http://dx.doi.org/10.1155/IJMMS.2005.2883 |
| work_keys_str_mv | AT ahansari moreonreversetriangleinequalityininnerproductspaces AT msmoslehian moreonreversetriangleinequalityininnerproductspaces |