Sentence examples for a function which approximately from inspiring English sources

A classical question in the theory of functional equations is that 'when is it true that a function which approximately satisfies a functional equation E Open image in new window must be somehow close to an exact solution of E Open image in new window.' Such a problem was formulated by Ulam [1] in 1940 and solved in the next year for the Cauchy functional equation by Hyers [2].

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 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 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 must be close to an exact solution of the equation?" If the problem accepts a solution, then we say that the equation is stable.

The key point is to show that a function which is "approximately harmonic", i.e. a function closes sufficiently to some harmonic function in ({L^{2}}).

Generally speaking, a function, which decreases approximately as a negative n-th power of the distance d, can be considered as the weight function.

But the technique of harmonic approximation is to show that a function which is "approximately-harmonic" lies close to some harmonic function.

In 1940, Ulam [1] proposed the following stability problem: 'When is it true that a function which satisfies some functional equation approximately must be close to one satisfying the equation exactly?'.

We say that a functional equation ℰ is stable if any function f which approximately satisfies the equation ℰ is near to an exact solution of ℰ.