Bernstein Polynomials and Modulus of Continuity

Some preservation properties of MKZ-Stancu type operators

“…Similar results for other univariate or multivariate operators can be found in [3], [8], [15] [16] and [17]. On the other hand, in [9] Li established that Bernstein polynomials also preserve the properties of the general function of the modulus of continuity which is related to smoothness. Cao, Ding and Xu [3] extended for the first time this result to the multivariate Baskakov operators.…”

On Certain Best Constants for Bernstein-Type Operators

“…L Remark 1. Against what happens in [11,4], the notion of a least concave majorant does not play any role in our developments. However, in connection with (2), it is worth noting that, when I= [0,1], the least concave majorant of the modulus w g e defined in (11) is given by…”

“…It should be said that, since B n (W) … W (n \ 1) (cf. [11]), and each w ¥ W coincides with its usual modulus of continuity, such a result can be viewed as a consequence of [4,Theorem 9 and the subsequent Remark (ii)].…”

“…On the other hand, in the same paper [11], the problem of determining whether or not C* < 2 is raised, C* being defined as C in (1) The author observes that the challenge of the problem comes from the fact that…”

Direct and inverse theorems for multivariate Bernstein-Schurer-Stancu operators

“…have been the most attractive approximating operators which were studied by various mathematicians and have many applications in mathematics, physics, engineering, economy, etc (see [3], [4], [7], [8], [9], [10], [11], [12], [14], [15], [17], [18], [19], [20], [21], [23]) . In the year 1962, Schurer [22] defined the Schurer operators as:…”