On the generalized Ulam-Gavruta-Rassias stability of mixed-type linear and Euler-Lagrange-Rassias functional equations.
On the global asymptotic stability of a second-order system of difference equations.
On the global attractivity of a max-type difference equation.
On the global character of the system of piecewise linear difference equations and .
On the graph of a quasi-additive function.
On the growth of nonoscillatory solutions for difference equations with deviating argument.
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 homogeneous difference equation in the field of Mikusiński operators.
On the Hyers-Ulam stability of quadratic functional equations.
On the hyperbolic linear functional equations.
On the identity of two -discrete Painlevé equations and their geometrical derivation.
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 inverse stability of functional equations
The inverse stability of functional equations is considered, i.e. when the function, approximating a solution of the equation, is an approximate solution of this equation.
On the Largest Solution of a Functional Equation Connected to sum Form Information Measures on Open Domain-i
On the linearization of second-order differential and difference equations.
On the lower hull of convex functions.
On the max-type difference equation .