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 |
| Published: |
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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