# Category: Functional equations

Abel equation
The Abel equation, named after Niels Henrik Abel, is a type of functional equation of the form or . The forms are equivalent when α is invertible. h or α control the iteration of f.
Iterated function
In mathematics, an iterated function is a function X → X (that is, a function from some set X to itself) which is obtained by composing another function f : X → X with itself a certain number of times
Hyers–Ulam–Rassias stability
The stability problem of functional equations originated from a question of Stanisław Ulam, posed in 1940, concerning the stability of group homomorphisms. In the next year, Donald H. Hyers gave a par
Superfunction
In mathematics, superfunction is a nonstandard name for an iterated function for complexified continuous iteration index. Roughly, for some function f and for some variable x, the superfunction could
Functional equation
In mathematics, a functional equation is, in the broadest meaning, an equation in which one or several functions appear as unknowns. So, differential equations and integral equations are functional eq
Cauchy–Rassias stability
A classical problem of Stanislaw Ulam in the theory of functional equations is the following: When is it true that a function which approximately satisfies a functional equation E must be close to an
Cauchy's functional equation
Cauchy's functional equation is the functional equation: A function that solves this equation is called an additive function. Over the rational numbers, it can be shown using elementary algebra that t
Schröder's equation
Schröder's equation, named after Ernst Schröder, is a functional equation with one independent variable: given the function h, find the function Ψ such that Schröder's equation is an eigenvalue equati
Functional equation (L-function)
In mathematics, the L-functions of number theory are expected to have several characteristic properties, one of which is that they satisfy certain functional equations. There is an elaborate theory of
Böttcher's equation
Böttcher's equation, named after Lucjan Böttcher, is the functional equation where * h is a given analytic function with a superattracting fixed point of order n at a, (that is, in a neighbourhood of
Functional square root
In mathematics, a functional square root (sometimes called a half iterate) is a square root of a function with respect to the operation of function composition. In other words, a functional square roo
Aequationes Mathematicae
Aequationes Mathematicae is a mathematical journal. It is primarily devoted to functional equations, but also publishes papers in dynamical systems, combinatorics, and geometry. As well as publishing
Aleksandrov–Rassias problem
The theory of isometries in the framework of Banach spaces has its beginning in a paper by Stanisław Mazur and Stanisław M. Ulam in 1932. They proved the Mazur–Ulam theorem stating that every isometry