On a functional inequality.
On a functional inequality arising in the construction of the product of several metric spaces.
On a modified Hyers-Ulam stability of homogeneous equation.
On a system of functional equations in a multi-dimensional domain.
On approximate cubic homomorphisms.
On associative copulas uniformly close.
On continuous convex or concave functions with respect to the logarithmic mean
On convex stochastic processes.
On convex triangle functions.
On functional inequalities in a single variable [Book]
On functions behaving like additive functions.
On functions with the Cauchy difference bounded by a functional. II.
On Functions with the Cauchy Difference Bounded by a Functional
K. Baron and Z. Kominek [2] have studied the functional inequality f(x+y) - f(x) - f(y) ≥ ϕ (x,y), x, y ∈ X, under the assumptions that X is a real linear space, ϕ is homogeneous with respect to the second variable and f satisfies certain regularity conditions. In particular, they have shown that ϕ is bilinear and symmetric and f has a representation of the form f(x) = ½ ϕ(x,x) + L(x) for x ∈ X, where L is a linear function. The purpose of the present...
On Hyers-Ulam stability for a class of functional equations.
On integral inequalities of the Sobolev type.
On Locally Subadditive Functions
On midpoint convex set-valued functions.
On Opial-type inequalities in two varaiables.
On separation theorems for subadditive and superadditive functionals
We generalize the well known separation theorems for subadditive and superadditive functionals to some classes of not necessarily Abelian semigroups. We also consider the problem of supporting subadditive functionals by additive ones in the not necessarily commutative case. Our results are motivated by similar extensions of the Hyers stability theorem for the Cauchy functional equation. In this context the so-called weakly commutative and amenable semigroups appear naturally. The relations between...
On solutions of functional equations determining subsemigroups of L¹₄
Let L¹₄ be the group of 4-jets at zero of diffeomorphisms f of ℝ with f(0) = 0. Identifying jets with sequences of derivatives, we determine all subsemigroups of L¹₄ consisting of quadruples (x₁,f(x₁,x₄),g(x₁,x₄),x₄) ∈ (ℝ∖{0}) × ℝ³ with continuous functions f,g:(ℝ∖{0}) × ℝ → ℝ. This amounts to solving a set of functional equations.