Approximation polynomiale des fonctions et analytiques
We introduce modified -Bernstein-Durrmeyer operators. We discuss approximation properties for these operators based on Korovkin type approximation theorem and compute the order of convergence using usual modulus of continuity. We also study the local approximation property of the sequence of positive linear operators and compute the rate of convergence for the function belonging to the class .
We establish direct estimates for the q-Baskakov operator introduced by Aral and Gupta in [2], using the second order Ditzian-Totik modulus of smoothness. Furthermore, we define and study the limit q-Baskakov operator.
Let be the best rational approximant to , 1 > α > 0, on [0,1] in the uniform norm. It is well known that all poles and zeros of lie on the negative axis . In the present paper we investigate the asymptotic distribution of these poles and zeros as n → ∞. In addition we determine the asymptotic distribution of the extreme points of the error function on [0,1], and survey related convergence results.