Let (S, +) be a commutative semigroup and let ζ be a proper left translation invariant σ-ideal in S. Suppose that f : S → R satisfies |f(x + y)| = |f(x) + f(y)| Ω(ζ)-almost everywhere in S x S. We prove that there exists, ...

In this paper certain functional inequalities are investigated whose solutions are shown to be convex provided that they are locally bounded from above. The results so obtained generalize the classical result of Bernstein ...

Transforms of linear functions in two variables are characterized via translation like composite functional equations on restricted domain, under regularity assumptions of C[1] type.

Let S be a closed convex cone such that int S ≠ 0 in a real separable Banach space. A necessary and sufficient condition is given under which a family {F[t] : t ≥ 0} of set-valued functions F[t] : S -> cc(S) is a concave ...

Let (Ω,Σ,μ) be a σ-finite space and Υ be a Banach space. It is shown that if F : (0,oo) → cl(Y) is a convex continuous set-valued function, then ∫[Ω]y{F°x/y)dμ ⊂ ∫[Ω]ydμF(∫[Ω]xdμ/∫[Ω]ydμ) for all positive p-integrable ...