AbstractWe prove direct and inverse theorems for the classical modulus of smoothness and approximation by algebraic polynomials in Lp[−1, 1]. These theorems contain the well-known theorems of A. Timan, V. Dzyadyk, G. Freud, and Yu. Brudnyi as special cases when p = ∞. They also provide a characterization of the spaces Lip(α, p) (Lipschitz spaces in Lp) for 0 < α < ∞, 1 ≤ p ≤ ∞
AbstractWe prove that for f ∈ Lp[−1, 1], 0 < p < 1 the modulus of smoothness τk(f, Δn)p,p introduced...
AbstractWe obtain uniform estimates for monotone and convex approximation of functions by algebraic ...
AbstractWe prove that for f ∈ Lp[−1, 1], 0 < p < 1 the modulus of smoothness τk(f, Δn)p,p introduced...
AbstractWe prove direct and inverse theorems for the classical modulus of smoothness and approximati...
We prove a direct theorem for convex polynomial L p-approximation, 0 < p < 1, in terms of the ...
AbstractWe prove converse and smoothness theorems of polynomial approximation in weightedLpspaces wi...
AbstractWe prove that for each convex function ƒ ∈ Lp, 0 < p < 1, there exists a convex algebraic po...
AbstractThe author introduced in an earlier paper a modulus of smoothness for nonperiodic functions ...
AbstractThe present paper investigates polynomials for which the inverse inequality for moduli of sm...
In this paper, we discuss various basic properties of moduli of smoothness of functions from Lp(Rd),...
AbstractIn this note a new characterization of smoothness is obtained for weighted polynomial approx...
Polynomial approximation on convex polytopes in \mathbf{R}^d is considered in uniform and L^p-norms....
AbstractThe best polynomial approximation is closely related to the Ditzian–Totik modulus of smoothn...
AbstractThe degree of approximation inLp-spaces by positive linear operators is estimated in terms o...
AbstractWe obtain uniform estimates for monotone and convex approximation of functions by algebraic ...
AbstractWe prove that for f ∈ Lp[−1, 1], 0 < p < 1 the modulus of smoothness τk(f, Δn)p,p introduced...
AbstractWe obtain uniform estimates for monotone and convex approximation of functions by algebraic ...
AbstractWe prove that for f ∈ Lp[−1, 1], 0 < p < 1 the modulus of smoothness τk(f, Δn)p,p introduced...
AbstractWe prove direct and inverse theorems for the classical modulus of smoothness and approximati...
We prove a direct theorem for convex polynomial L p-approximation, 0 < p < 1, in terms of the ...
AbstractWe prove converse and smoothness theorems of polynomial approximation in weightedLpspaces wi...
AbstractWe prove that for each convex function ƒ ∈ Lp, 0 < p < 1, there exists a convex algebraic po...
AbstractThe author introduced in an earlier paper a modulus of smoothness for nonperiodic functions ...
AbstractThe present paper investigates polynomials for which the inverse inequality for moduli of sm...
In this paper, we discuss various basic properties of moduli of smoothness of functions from Lp(Rd),...
AbstractIn this note a new characterization of smoothness is obtained for weighted polynomial approx...
Polynomial approximation on convex polytopes in \mathbf{R}^d is considered in uniform and L^p-norms....
AbstractThe best polynomial approximation is closely related to the Ditzian–Totik modulus of smoothn...
AbstractThe degree of approximation inLp-spaces by positive linear operators is estimated in terms o...
AbstractWe obtain uniform estimates for monotone and convex approximation of functions by algebraic ...
AbstractWe prove that for f ∈ Lp[−1, 1], 0 < p < 1 the modulus of smoothness τk(f, Δn)p,p introduced...
AbstractWe obtain uniform estimates for monotone and convex approximation of functions by algebraic ...
AbstractWe prove that for f ∈ Lp[−1, 1], 0 < p < 1 the modulus of smoothness τk(f, Δn)p,p introduced...
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