Ternary Jordan homomorphisms in -ternary algebras.
The Abel equation and total solvability of linear functional equations
We investigate the solvability in continuous functions of the Abel equation φ(Fx) - φ(x) = 1 where F is a given continuous mapping of a topological space X. This property depends on the dynamics generated by F. The solvability of all linear equations P(x)ψ(Fx) + Q(x)ψ(x) = γ(x) follows from solvability of the Abel equation in case F is a homeomorphism. If F is noninvertible but X is locally compact then such a total solvability is determined by the same property of the cohomological equation φ(Fx)...
The associativity equation revisited.
The Christensen measurable solutions of a generalization of the Gołąb-Schinzel functional equation
Let K denote the set of all reals or complex numbers. Let X be a topological linear separable F-space over K. The following generalization of the result of C. G. Popa [16] is proved. Theorem. Let n be a positive integer. If a Christensen measurable function f: X → K satisfies the functional equation , then it is continuous or the set x ∈ X : f(x) ≠ 0 is a Christensen zero set.
The cocycle equation in division rings.
The cosine functional equation for nilpotent groups.
The cosine functional equation for nilpotent groups. (Short Communication).
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).