函数论的一个重要组成部分，涉及的基本问题是函数的近似表示问题。在数学的理论研究和实际应用中经常遇到下类问题：在选定的一类函数中寻找某个函数g，使它是已知函数?在一定意义下的近似表示，并求出用g近似表示 ?而产生的误差。这就是函数逼近问题。在函数逼近问题中，用来逼近已知函数?的函数类可以有不同的选择；即使函数类选定了，在该类函数中用作?的近似表示的函数g的确定方式仍然是各式各样的；g对?的近似程度（误差）也可以有各种不同的含义。所以函数逼近问题的提法具有多样的形式，其内容十分丰富。(An important part of the functional theory involves the basic problem of the approximate representation of functions. Such problems often encountered in theoretical research and practical application of mathematics in search of a G function in a class of functions selected, it is known that the function f more approximate in some sense representation, and gives the representation f more using the G approximation error and produce. This is the function approximation problem. In function approximation, used to approximate the given function f more functions can have different choices; even if the function is selected, in this kind of function is used as the approximate representation of the function f more G is still the way to determine the approximate degree of every kind of G; the f more (error) can also have various meanings. Therefore, the formulation of the function approximation problem has various forms, and its content is very rich.)