Add to ORKGWe introduce appropriate computable moduli of smoothness to characterize the rate of best approximation by multivariate polynomials on a connected and compact $C^2$-domain $\Omega\subset \mathbb{R}^d$. This new modulus of smoothness is defined via finite differences along the directions of coordinate axes, and along a number of tangential directions from the boundary. With this modulus, we prove both the direct Jackson inequality and the corresponding inverse for the best polynomial approximation in $L_p(\Omega)$. The Jackson inequality is established for the full range of $0<p\leq \infty$, while its proof relies on a recently established Whitney type estimates with constants depending only on certain parameters; and on a highly localized p...
An analog of the Jackson Chernykh inequality for spline approximations in the space L2(R) is establ...
Abstract. Let f ∈ C[−1, 1] change its convexity finitely many times in the interval, say s times, at...
Abstract. For a compact set K which is the closure of a Jordan domain, the Faber operator provides a...
AbstractWe prove direct and inverse theorems for the classical modulus of smoothness and approximati...
When we approximate a function f in which changes its monotonicity finitely many, say s time, in...
summary:We show that a $C^k$-smooth mapping on an open subset of $\mathbb R^n$, $k\in \mathbb N\cup\...
AbstractWe state some pointwise estimates for the rate of weighted approximation of a continuous fun...
AbstractThe author introduced in an earlier paper a modulus of smoothness for nonperiodic functions ...
AbstractWe prove a multivariate Whitney type theorem for the local anisotropic polynomial approximat...
AbstractThe present paper investigates polynomials for which the inverse inequality for moduli of sm...
Polynomial approximation on convex polytopes in \mathbf{R}^d is considered in uniform and L^p-norms....
Abstract. It has been proved [7] that discrete least squares polynomial approximation performed on (...
AbstractIn 1934, Walsh noted that the Taylor polynomial of degree n can be obtained by taking the li...
We study the Lusin approximation problem for real-valued measurable functions on Carnot groups. We p...
AbstractWe obtain sufficient conditions on a real valued function ƒ, continuous on [0, + ∞), to insu...
An analog of the Jackson Chernykh inequality for spline approximations in the space L2(R) is establ...
Abstract. Let f ∈ C[−1, 1] change its convexity finitely many times in the interval, say s times, at...
Abstract. For a compact set K which is the closure of a Jordan domain, the Faber operator provides a...
AbstractWe prove direct and inverse theorems for the classical modulus of smoothness and approximati...
When we approximate a function f in which changes its monotonicity finitely many, say s time, in...
summary:We show that a $C^k$-smooth mapping on an open subset of $\mathbb R^n$, $k\in \mathbb N\cup\...
AbstractWe state some pointwise estimates for the rate of weighted approximation of a continuous fun...
AbstractThe author introduced in an earlier paper a modulus of smoothness for nonperiodic functions ...
AbstractWe prove a multivariate Whitney type theorem for the local anisotropic polynomial approximat...
AbstractThe present paper investigates polynomials for which the inverse inequality for moduli of sm...
Polynomial approximation on convex polytopes in \mathbf{R}^d is considered in uniform and L^p-norms....
Abstract. It has been proved [7] that discrete least squares polynomial approximation performed on (...
AbstractIn 1934, Walsh noted that the Taylor polynomial of degree n can be obtained by taking the li...
We study the Lusin approximation problem for real-valued measurable functions on Carnot groups. We p...
AbstractWe obtain sufficient conditions on a real valued function ƒ, continuous on [0, + ∞), to insu...
An analog of the Jackson Chernykh inequality for spline approximations in the space L2(R) is establ...
Abstract. Let f ∈ C[−1, 1] change its convexity finitely many times in the interval, say s times, at...
Abstract. For a compact set K which is the closure of a Jordan domain, the Faber operator provides a...