林阿婵1991年给出Hölder度量下Jackson多项式的逼近与饱和定理,在此基础上,本文运用度量定义、连续模的性质、Jackson多项式的插值特性,再结合不等式的放缩方法,解决了如下问题：一个函数所生成的Jackson多项式与该函数之差在广义Hölder度量下的范数若要达到一定的阶,函数及其共轭函数所要满足的条件.最后给出了广义Hölder度量下Jackson多项式逼近与饱和的两个结果,建立了更广泛适用的理论.

In the year of 1991, Lin Achan established a theory about the approximation and saturation of Jackson polynomial under Hölder metric. On the basis of those results,Jackson polynomial has been approximated under the generalized Hölder metric by using metric definition, modulus property, and interpolation feature of Jackson polynomial combining with the method of magnifying or diminishing inequality, the theory is effective proved. The following question is solved, namely, for a norm of the subtraction between function and its corresponding Jackson polynomial under generalized Hölder metric attains the certain degree, what kind of condition function and its conjugate function have to satisfy? In the end, two results about approximation and saturation of Jackson polynomial under generalized Hölder metric are obtained, which is more extensive than quondam conclusion.