The Euler-Maclaurin sum formula for an inner derivation.
The Feigenbaum functional equation and periodic points.
The Feigenbaum functional equation and periodic points. (Short Communication).
The fixed point method for fuzzy approximation of a functional equation associated with inner product spaces.
The functional equation F(ax) + F(bx+a) = F(bx) + F(ax+b), entire and almost periodic solutions.
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 linear equation on vector spaces.
The general solution of a functional equation in two variables.
The general solution of a functional equation related to the mixed theory of information.
The general solution of the generalized Schilling's equation.
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 geometry of convex cones associated with the Lyapunov inequality and the common Lyapunov function problem.
The Hyers-Ulam stability for two functional equations in a single variable.
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 law of large numbers and a functional equation
We deal with the linear functional equation (E) , where g:(0,∞) → (0,∞) is unknown, is a probability distribution, and ’s are positive numbers. The equation (or some equivalent forms) was considered earlier under different assumptions (cf. [1], [2], [4], [5] and [6]). Using Bernoulli’s Law of Large Numbers we prove that g has to be constant provided it has a limit at one end of the domain and is bounded at the other end.