On the graph of a quasi-additive function.
On the helix equation
This paper is devoted to the helices processes, i.e. the solutions H : ℝ × Ω → ℝd, (t, ω) ↦ H(t, ω) of the helix equation where Φ : ℝ × Ω → Ω, (t, ω) ↦ Φ(t, ω) is a dynamical system on a measurable space (Ω, ℱ).More precisely, we investigate dominated solutions and non differentiable solutions of the helix equation. For the last case, the Wiener helix plays a fundamental role. Moreover, some relations with the cocycle equation defined...
On the Heyde theorem for discrete Abelian groups
Let X be a countable discrete Abelian group, Aut(X) the set of automorphisms of X, and I(X) the set of idempotent distributions on X. Assume that α₁, α₂, β₁, β₂ ∈ Aut(X) satisfy . Let ξ₁, ξ₂ be independent random variables with values in X and distributions μ₁, μ₂. We prove that the symmetry of the conditional distribution of L₂ = β₁ξ₁ + β₂ξ₂ given L₁ = α₁ξ₁ + α₂ξ₂ implies that μ₁, μ₂ ∈ I(X) if and only if the group X contains no elements of order two. This theorem can be considered as an analogue...
On the homogeneity of additive mappings.
On the Hyers-Ulam stability of quadratic functional equations.
On the increasing solutions of the translation equation
Let M be a non-empty set endowed with a dense linear order without the smallest and greatest elements. Let (G,+) be a group which has a non-trivial uniquely divisible subgroup. There are given conditions under which every solution F: M×G → M of the translation equation is of the form for a ∈ M, x ∈ G with some non-trivial additive function c: G → ℝ and a strictly increasing function f: M → ℝ such that f(M) + c(G) ⊂ f(M). In particular, a problem of J. Tabor is solved.
On the inhomogeneous Cauchy functional equation.
In this note we solve the inhomogeneous Cauchy functional equation f(x+y) - f(x) - f(y) = d(x,y), x,y belonging to R, in the case where d is bounded.
On the order of exponential growth of the solution of the linear difference equation with periodic coefficient in Banach space.
On the Pexider difference
On the Pexider equation.
On the pseudo-processes and pseudo-dynamical systems
On the stability of a general mixed additive-cubic functional equation in random normed spaces.
On the stability of a generalized quadratic and quartic type functional equation in quasi-Banach spaces.
On the stability of cubic mappings and quadratic mappings in random normed spaces.
On the stability of Drygas functional equation on groups.
On the stability of generalized additive functional inequalities in Banach spaces.
On the stability of generalized d'Alembert and Jensen functional equations.
On the stability of generalized quartic mappings in quasi--normed spaces.
On the stability of mixed trigonometric functional equations.
On the stability of quadratic functional equations.