On Cubature Formulae with a Minimal Number of Knots.
On degrees of approximation of some classes by polynomials with respect to generalized Haar system.
On difference equations and discrete systems
On differentiability properties of Lipschitz functions on a Banach space with a Lipschitz uniformly Gâteaux differentiable bump function
We improve a theorem of P.G. Georgiev and N.P. Zlateva on Gâteaux differentiability of Lipschitz functions in a Banach space which admits a Lipschitz uniformly Gâteaux differentiable bump function. In particular, our result implies the following theorem: If is a distance function determined by a closed subset of a Banach space with a uniformly Gâteaux differentiable norm, then the set of points of at which is not Gâteaux differentiable is not only a first category set, but it is even -porous...
On differentiation of metric projections in finite dimensional Banach spaces
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 embeddings and traces in Sobolev spaces with weights of power type
On embeddings of function classes defined by constructive characteristics
In this paper we study embedding theorems for function classes which are subclasses of , 1 ≤ p ≤ ∞. To define these classes, we use the notion of best trigonometric approximation as well as that of a (λ,β)-derivative, which is the generalization of a fractional derivative. Estimates of best approximations of transformed Fourier series are obtained.
On Equally Weighted Quadratures.
On equivalence question between the Ditzian-Totik modulus of smoothness and an usual periodic modulus of smoothness.
On error bounds for Gauss-Legendre and Lobatto quadrature rules.
On error estimates for interpolating splines with minimal defect
On error formulas for approximation by sums of univariate functions.
On estimates for the moduli of smoothness of functions with a transformed Fourier series.
On Existence of Finite Universal Korovkin Sets in the Centre of Group Algebras.
On exponential approximation
On extremal problems related to inverse balayage.
On extremum-searching approximate probabilistic algorithms
On -best approximation in topological spaces