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In mathematics, a functional equation [1] [2] [irrelevant citation] is, in the broadest meaning, an equation in which one or several functions appear as unknowns. So, differential equations and integral equations are functional equations.
Download as PDF; Printable version; ... This is a list of equations, by Wikipedia page under ... Functional equation (L-function) Lists of equations
That is, a functional differential equation is an equation that contains a function and some of its derivatives evaluated at different argument values. [ 1 ] Functional differential equations find use in mathematical models that assume a specified behavior or phenomenon depends on the present as well as the past state of a system. [ 2 ]
These equations for solution of a first-order partial differential equation are identical to the Euler–Lagrange equations if we make the identification = ˙ ˙. We conclude that the function ψ {\displaystyle \psi } is the value of the minimizing integral A {\displaystyle A} as a function of the upper end point.
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 [1] gave a partial affirmative answer to the question of Ulam in the context of Banach spaces in the case of additive mappings, that was the first significant breakthrough and a step toward more solutions ...
Download as PDF; Printable version; In other projects Wikidata item; ... Pages in category "Functional equations" The following 13 pages are in this category, out of ...
In functional analysis and related fields, it refers to a mapping from a space into the field of real or complex numbers. [2] [3] In functional analysis, the term linear functional is a synonym of linear form; [3] [4] [5] that is, it is a scalar-valued linear map.
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 there is a single family of solutions, namely : for any rational constant .