On the impossibility of approximating convex functions with ones.
Direct approximation theorems for discrete type operators.
Direct and Converse Theorems for Generalized Bernstein-Type Operators
2000 Mathematics Subject Classification: 41A25, 41A27, 41A36. We establish direct and converse theorems for generalized parameter dependent Bernstein-type operators. The direct estimate is given using a K-functional and the inverse result is a strong converse inequality of type A, in the terminology of [2].
Bernstein type operators having 1 and x j as fixed points
For certain generalized Bernstein operators {L n} we show that there exist no i, j ∈ {1, 2, 3,…}, i < j, such that the functions e i(x) = x i and e j (x) = x j are preserved by L n for each n = 1, 2,… But there exist infinitely many e i such that e 0(x) = 1 and e j (x) = x j are its fixed points.
Approximation by -Bernstein type operators
Using the -Bernstein basis, we construct a new sequence of positive linear operators in We study its approximation properties and the rate of convergence in terms of modulus of continuity.
Approximation properties of q-Baskakov operators
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.
Page 1