Monotone approximation with linear differential operators (Q1061962)

The subject of monotone approximation initiated by the second author in Pac. J. Math. 15, 667-671 (1965; Zbl 0148.293) has become a major trend in approximation theory. A typical problem in this subject is: given a positive integer k, approximate a given function whose kth derivative is \(\geq 0\) by polynomials having this property. We generalize this problem by replacing the kth derivative with a linear differential operator of order k.