The Euler-Maclaurin sum formula for an inner derivation.
The fixed point method for fuzzy approximation of a functional equation associated with inner product spaces.
The functional equation f(xy) = ff(x) xy ff(y) in a partially ordered monoid.
The functional equation of distance preservance in spaces over rings.
The functional equation of distance preservance in spaces over rings. (Short Communication).
The fundamental equation of information and its generalizations.
The general solution of a functional equation in two variables.
The generalized Cauchy equation for operator-valued functions.
The generalized Cauchy equation for operator-valued functions. (Short Communication).
The generalized Hyers-Ulam-Rassias stability of a quadratic functional equation.
The Hyers-Ulam-Aoki Type Stability of Some Functional Equations on Banach Lattices
In Agbeko (2012) the Hyers-Ulam-Aoki stability problem was posed in Banach lattice environments with the addition in the Cauchy functional equation replaced by supremum. In the present note we restate the problem so that it relates not only to supremum but also to infimum and their various combinations. We then propose some sufficient conditions which guarantee its solution.
The Levi-Civita equation, vector modules and spectral synthesis
The purpose of this paper is to give a survey on some recent results concerning spectral analysis and spectral synthesis in the framework of vector modules and in close connection with the Levi-Civita functional equation. Further, we present some open problems in this subject.
The matrix equation a(x...y) = a(x) + a(x)a(y) + a(y).
The order-independence of the polylogarithmic ladder structure - implications for a new category of functional equations.
The real-analytic solutions of the Abel functional equation
For the Abel equation on a real-analytic manifold a dynamical criterion of solvability in real-analytic functions is proved.
The solution of a system of quadratic functional equations
The solution of the functional equation of d'Alembert's type for commutative groups.
The stability of a quadratic functional equation with the fixed point alternative.
The stability of some linear functional equations.
The stability of the equation on groups.