A basic question in the theory of functional equations is as follows: when is it true that a function, which approximately satisfies a functional equation, must be close to an exact solution of the equation?
A classical question 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 exact solution of ℰ?
A classical question in the theory of functional equations is the following: 'When is it true that a function which approximately satisfies a functional equation D must be close to an exact solution of D?'.
A classical question in the theory of functional equations is the following: "When is it true that a function which approximately satisfies a functional equation must be close to an exact solution of the equation?".
A classical question in the theory of functional equations is the following: 'When is it true that a function which approximately satisfies a functional equation must be close to an exact solution of the equation?' If the problem accepts a solution, we say that the equation is stable.
We also give a functional equation for the generating function.
In 2006, Crabb [26] showed that Gessel's generalization of Miki's identity [27] is a direct consequence of a functional equation for the generating function.
The simplest problem of this kind is the classical two-part problem which can be reduced to a functional equation involving two unknown functions, say Ψ+ and Ψ−, which are regular in the upper and lower halves of the complex ν-plane, respectively.
Theorem 2.2 ∑ s = 0 n ( − 1 ) s S n ( 1, s, x ) = 2 1 − n ( 2 − 3 x ) n. Here, we give partial differential equations and a functional equation of the generating function for the unification of the Bernstein-type polynomials S n ( b, s, x ).
A functional equation is superstable if any function g satisfying the equation approximately is a true solution of.
We say a functional equation is stable if any function g satisfying the equation approximately is near to a true solution of.
