On functions with the Cauchy difference bounded by a functional. Part II

Włodzimierz Fechner

International Journal of Mathematics and Mathematical Sciences, 2005, vol. 2005, 1-10

Abstract:

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).

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:629421

DOI: 10.1155/IJMMS.2005.1889

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