Sentence examples for approximately a functional from inspiring English sources

Summing up the above, the Ulam type stability problem is whether, for a given mapping which satisfies approximately a functional equation (or which satisfies a functional inequality), there exists an exact solution of the corresponding functional equation such that the preceding mapping is sufficiently close to this solution.

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?".

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.

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.

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 "when is it true that a mapping, which approximately satisfies a functional equation, must be somehow close to an exact solution of the equation?".

A classical question in the theory of functional equations is that "when is it true that a mapping which approximately satisfies a functional equation must be somehow close to an exact solution of ?" Such a problem was formulated by Ulam [6] in 1940 and solved in the next year for the Cauchy functional equation by Hyers [7].

The following question posed by Ulam [1] in 1940: "When is it true that a mapping which approximately satisfies a functional equation E must be somehow close to an exact solution of E ?". Hyers [2] proved the problem for the Cauchy functional equation.