Hyers-Ulam stability of functional equations in several variables.
On an alternative functional equation related to the Cauchy equation. (Short Communication).
On an alternative functional equation related to the Cauchy equation.
The general solution of a functional equation in two variables.
A note on a general difference-functional equation.
An existence and stability theorem for a class of functional equations.
Consider the class of functional equations g[F(x,y)] = H[g(x),g(y)], where g: E --> X, f: E x E --> E, H: X x X --> X, E is a set and (X,d) is a complete metric space. In this paper we prove that, under suitable hypotheses on F, H and ∂(x,y), the existence of a solution of the functional inequality d(f[F(x,y)],H[f(x),f(y)]) ≤ ∂(x,y), implies the existence of a solution of the above equation.
A system on functional equations related to plurality functions. A method for the construction of the solutions. (Summary).
On an alternative Cauchy equation in two unknown functions. Some classes of solutions.
A system of functional equations related to plurality functions. A method for the construction of the solutions.
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 a general Hyers-Ulam stability result.
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