一类保持线性函数的算子的逼近

Approximation of a class of operators preserving linear functions

自Phillips G M1997年构造研究q-Bermstein算子以来,q-微积分于逼近论中的应用研究成为热点. Gupta V于2018年建立并研究了著名的Durrmeyer算子的q-模拟.任美英于2021年引进并研究了只保持常数的修正q-Durrmeyer型算子逼近.基于q-整数概念和q-微积分理论,引进一类能保持线性函数的算子,并对该算子列的逼近性质加以研究.得到算子列的Korovkin型收敛定理,并给出其收敛速度的若干估计.

Since Phillips G.M.constructed and studied q-Bernstein operators in 1997,the application of q-calculus in approximation theory has become a research hotspot.Gupta V.established and studied the q-analogue of the famous Durrmeyer operator in 2018.Ren Mei-ying introduced and studied the modified q-Durrmeyer type operator approximation which only keeps constant in 2021.In this paper, based on the concept of q-integer and the theory of q-calculus, a class of operators preserving linear function is introduced, and some approximation properties of the operator sequence are studied.A Korovkin type convergence theorem for operator sequences is obtained, and some estimates of the rate of convergence are given.