3 research outputs found
On the Hyers–Ulam stability of functional equations connected with additive and quadratic mappings
AbstractWe investigate some inequalities connected with the Hyers–Ulam stability of three functional equations, which have a solution of the form φ=a+q, where a is an additive mapping and q is a quadratic one
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, where
a is an additive function. In the present paper, we continue and
develop our earlier studies published by the
author (2004)