Almost midconvex and almost convex set-valued functions
Almost periodicity and functional equations.
Almost Trivial Groupoids
Almost -convex and almost Wright-convex functions
An algebraic functional equation
An analytic representation for selfmaps of a countably infinite set and its cycles. (Short Communication).
An analytic representation for selfmaps of a countably infinite set and its cycles.
An application of a functional equation to information theory
An application of nonstandard analysis to functional equations.
An asymptotic form of Cauchy's functional equation.
An asymptotic form of Cauchy's functional equation. (Short Communication).
An axiomatic characterization of generalized directed-divergence
An axiomatization of Nesterenko's method and applications on Mahler functions II
An example of a stable functional equation when the Hyers method does not work.
An existence and stability theorem for a class of functional equations.
Consider the class of functional equationsg[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 inequalityd(f[F(x,y)],H[f(x),f(y)]) ≤ ∂(x,y),implies the existence of a solution of the above equation.
An expanded class of parametric partial linear complex vector functional equations.
An extension theorem.
An extension theorem for a Matkowski-Sutô problem
Let I be an interval, 0 < λ < 1 be a fixed constant and A(x,y) = λx + (1-λ)y, x,y ∈ I, be the weighted arithmetic mean on I. A pair of strict means M and N is complementary with respect to A if A(M(x,y),N(x,y)) = A(x,y) for all x, y ∈ I. For such a pair we give results on the functional equation f(M(x,y)) = f(N(x,y)). The equation is motivated by and applied to the Matkowski-Sutô problem on complementary weighted quasi-arithmetic means M and N.
An inconsistency equation involving means
We show that any quasi-arithmetic mean and any non-quasi-arithmetic mean M (reasonably regular) are inconsistent in the sense that the only solutions f of both equations and are the constant ones.
An initial value problem for a functiona equation.