Lipschitz constants for the Bernstein polynomials of a Lipschitz continuous function

Bernstein Polynomials and Modulus of Continuity

“…The proofs of (iii)*, (iv), and (v) are elementary and those of (iii)* and (iv) are only based on the following two representations of the Bernstein polynomial B n ( f ; x) derived in [2],…”

Preservation of Lipschitz constants by Bernstein type operators

“…In [6] in a purely algebraic way this last result is obtained for 0 < µ 1 and it is also proved that the inequality θ…”

Best Constants in Preservation Inequalities Concerning the First Modulus and Lipschitz Classes for Bernstein-Type Operators

“…Better estimates for more general families can be found in [1]. On the other hand, Lindvall [12] and Brown, Elliott and Paget [6], among others, have shown that the Bernstein polynomials preserve Lipschitz constants. In a more general setting, a probabilistic approach to this problem is given in [1,10].…”