On functions with the Cauchy difference bounded by a functional. Part II
We are going to consider the functional inequality f(x+y)−f(x)−f(y)≥ϕ(x,y), x,y∈X, where (X,+) is an abelian group, and ϕ:X×X→ℝ and f:X→ℝ are unknown mappings. In particular, we will give conditions which force biadditivity and symmetry of ϕ and the representation f(x)=(1/2)ϕ(x,x)+a(x) for x∈X, wher...
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| Format: | Article |
| Language: | English |
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Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.1889 |
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| _version_ | 1832565434026557440 |
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| author | Włodzimierz Fechner |
| author_facet | Włodzimierz Fechner |
| author_sort | Włodzimierz Fechner |
| collection | DOAJ |
| description | We are going to consider the functional inequality f(x+y)−f(x)−f(y)≥ϕ(x,y), x,y∈X, where (X,+) is an abelian
group, and ϕ:X×X→ℝ and f:X→ℝ are unknown mappings. In particular, we will give conditions
which force biadditivity and symmetry of ϕ and the
representation f(x)=(1/2)ϕ(x,x)+a(x) for x∈X, where
a is an additive function. In the present paper, we continue and
develop our earlier studies published by the
author (2004). |
| format | Article |
| id | doaj-art-2eac7bf5c8804734826e6cec6d6ee189 |
| 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-2eac7bf5c8804734826e6cec6d6ee1892025-02-03T01:07:47ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-012005121889189810.1155/IJMMS.2005.1889On functions with the Cauchy difference bounded by a functional. Part IIWłodzimierz Fechner0Institute of Mathematics, Faculty of Mathematics, Physics and Chemistry, University of Silesia, 14 Bankowa Street, Katowice 40-007, PolandWe are going to consider the functional inequality f(x+y)−f(x)−f(y)≥ϕ(x,y), x,y∈X, where (X,+) is an abelian group, and ϕ:X×X→ℝ and f:X→ℝ are unknown mappings. In particular, we will give conditions which force biadditivity and symmetry of ϕ and the representation f(x)=(1/2)ϕ(x,x)+a(x) for x∈X, where a is an additive function. In the present paper, we continue and develop our earlier studies published by the author (2004).http://dx.doi.org/10.1155/IJMMS.2005.1889 |
| spellingShingle | Włodzimierz Fechner On functions with the Cauchy difference bounded by a functional. Part II International Journal of Mathematics and Mathematical Sciences |
| title | On functions with the Cauchy difference bounded by a functional. Part II |
| title_full | On functions with the Cauchy difference bounded by a functional. Part II |
| title_fullStr | On functions with the Cauchy difference bounded by a functional. Part II |
| title_full_unstemmed | On functions with the Cauchy difference bounded by a functional. Part II |
| title_short | On functions with the Cauchy difference bounded by a functional. Part II |
| title_sort | on functions with the cauchy difference bounded by a functional part ii |
| url | http://dx.doi.org/10.1155/IJMMS.2005.1889 |
| work_keys_str_mv | AT włodzimierzfechner onfunctionswiththecauchydifferenceboundedbyafunctionalpartii |