MKZ型算子中心矩的明确上界估计

MKZ型算子及其各类变型算子在逼近论中占据重要地位．若计算其各阶中心矩，其上界估计式需要首先给出．但是，由于算子本身计算复杂度很高，仅仅是其二阶矩的粗略估计和明确估计分别是在18年和35年之后才有人给出．而其各阶矩的粗略估计更是在近半个世纪之后得到的．参考已有研究成果，利用新的逼近技巧给出MKZ型算子各阶矩的明确上界估计．

Explicit Upper Bound Estimates of Central Moments on MKZ-Type Operators

The MKZ-type operators and their modified operators play an essential role in approximation theory. Their upper bound estimates need to be given first if the all order central moments on these operators are to be computed. Due to the difficulty of computing these operators, their rough estimates and explicit estimates of second-order mo- ments were given after 18 years and 35 years, respectively. Furthermore, the rough estimates of all-order moments on these operators were given after about a half of century. By applying existing results and new approximation knowledge, the explicit upper bound estimates of all-order moments on MKZ-type operators has been derived.