Functional Inequalities Associated with Additive Mappings
The functional inequality ‖f(x)+2f(y)+2f(z)‖≤‖2f(x/2+y+z)‖+ϕ (x,y,z) (x,y,z∈G) is investigated, where G is a group divisible by 2,f:G→X and ϕ:G3→[0,∞) are mappings, and X is a Banach space. The main result of the paper states that the assumptions above together with (1) ϕ(2x,−x,0)=0=ϕ(0,x,−x) (x∈G)...
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2008/136592 |
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| _version_ | 1849306564510351360 |
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| author | Jaiok Roh Ick-Soon Chang |
| author_facet | Jaiok Roh Ick-Soon Chang |
| author_sort | Jaiok Roh |
| collection | DOAJ |
| description | The functional inequality ‖f(x)+2f(y)+2f(z)‖≤‖2f(x/2+y+z)‖+ϕ (x,y,z) (x,y,z∈G) is investigated, where G is a group divisible by 2,f:G→X and ϕ:G3→[0,∞) are mappings, and X is a Banach space. The main result of the paper states that the assumptions above together with (1) ϕ(2x,−x,0)=0=ϕ(0,x,−x) (x∈G) and (2) limn→∞(1/2n)ϕ(2n+1x,2ny,2nz)=0, or limn→∞2nϕ(x/2n−1,y/2n,z/2n)=0 (x,y,z∈G), imply that f is additive. In addition, some stability theorems are proved. |
| format | Article |
| id | doaj-art-36f0975179e1438aa031c2386ccb8fdf |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-36f0975179e1438aa031c2386ccb8fdf2025-08-20T03:55:02ZengWileyAbstract and Applied Analysis1085-33751687-04092008-01-01200810.1155/2008/136592136592Functional Inequalities Associated with Additive MappingsJaiok Roh0Ick-Soon Chang1Department of Mathematics, Hallym University, Chuncheon 200-702, South KoreaDepartment of Mathematics, Mokwon University, Daejeon 302-729, South KoreaThe functional inequality ‖f(x)+2f(y)+2f(z)‖≤‖2f(x/2+y+z)‖+ϕ (x,y,z) (x,y,z∈G) is investigated, where G is a group divisible by 2,f:G→X and ϕ:G3→[0,∞) are mappings, and X is a Banach space. The main result of the paper states that the assumptions above together with (1) ϕ(2x,−x,0)=0=ϕ(0,x,−x) (x∈G) and (2) limn→∞(1/2n)ϕ(2n+1x,2ny,2nz)=0, or limn→∞2nϕ(x/2n−1,y/2n,z/2n)=0 (x,y,z∈G), imply that f is additive. In addition, some stability theorems are proved.http://dx.doi.org/10.1155/2008/136592 |
| spellingShingle | Jaiok Roh Ick-Soon Chang Functional Inequalities Associated with Additive Mappings Abstract and Applied Analysis |
| title | Functional Inequalities Associated with Additive Mappings |
| title_full | Functional Inequalities Associated with Additive Mappings |
| title_fullStr | Functional Inequalities Associated with Additive Mappings |
| title_full_unstemmed | Functional Inequalities Associated with Additive Mappings |
| title_short | Functional Inequalities Associated with Additive Mappings |
| title_sort | functional inequalities associated with additive mappings |
| url | http://dx.doi.org/10.1155/2008/136592 |
| work_keys_str_mv | AT jaiokroh functionalinequalitiesassociatedwithadditivemappings AT icksoonchang functionalinequalitiesassociatedwithadditivemappings |