Nonnegative order iterates of Bernstein polynomials and their limiting semigroup
Note on the first order orthogonal projections
Numerical integration with weights of convex functions of algebraic polynomials
On a general class of linear and positive operators.
On an approximation of function and its derivatives.
On an Interpolation Process of Lagrange-Hermite Type
On an orthonormal polynomial basis in the space C[-1,1]
We show that in the space C[-1,1] there exists an orthogonal algebraic polynomial basis with optimal growth of degrees of the polynomials.
On approximation by modified Bernstein polynomials.
On Approximation Of Continuous And Differentiable Functions By Fourier-Jacobi Series
On Bernstein inequalities for multivariate trigonometric polynomials in ,
Let be the space of all trigonometric polynomials of degree not greater than with complex coefficients. Arestov extended the result of Bernstein and others and proved that for and . We derive the multivariate version of the result of Golitschek and Lorentz for all trigonometric polynomials (with complex coeffcients) in variables of degree at most .
On Best Error Bounds for Approximation by Piecewise Polynomial Functions.
On Certain Problems of Chebyshev, Zolotarev, Bernstein and Akhieser.
On constrained uniform approximation.
On convex Bézier triangles
On Direct and Converse Theorems in the Theory of Weighted Poynomial Approximation.
On discrepancy theorems with applications to approximation theory
We give an overview on discrepancy theorems based on bounds of the logarithmic potential of signed measures. The results generalize well-known results of P. Erdős and P. Turán on the distribution of zeros of polynomials. Besides of new estimates for the zeros of orthogonal polynomials, we give further applications to approximation theory concerning the distribution of Fekete points, extreme points and zeros of polynomials of best uniform approximation.
On equivalence question between the Ditzian-Totik modulus of smoothness and an usual periodic modulus of smoothness.
On global smoothness preservation in complex approximation
By using the properties of convergence and global smoothness preservation of multivariate Weierstrass singular integrals, we establish multivariate complex Carleman type approximation results with rates. Here the approximants fulfill the global smoothness preservation property. Furthermore Mergelyan's theorem for the unit disc is strengthened by proving the global smoothness preservation property.
On Hermite interpolation formula.
On interpolation polynomials of the Hermite-Fejér type