Remarks on monotone and convex approximation by algebraic polynomials

Abstract

The following results are obtained: If and is a nondecreasing (convex) function on [-1,1] such that for any then for and , where is the value of the best uniform approximation of a continuous function by polynomials of degree , and and are the values of the best monotone and convex approximation, respectively. For and , this result is not true.