Nearly Comonotone Approximation

John A. Roulier
1975 Proceedings of the American Mathematical Society  
This paper obtains estimates on the degree of nearly comonotone approximation which extend and improve the estimate obtained by Newman, Passow, and Raymon. In particular, the restriction that / e LipM 1 is removed, and estimates for the degree of nearly comonotone approximation are obtained for all proper piecewise monotone functions. It is also shown that if / exists and is continuous on the interval, then the ordinary polynomials of best approximation form a nearly comonotone sequence.
doi:10.2307/2040212 fatcat:t4wj3b2gxvcyfo25kbqzq7td4a