AbstractA convex function f given on [−1, 1] can be approximated in Lp, 1 < p < ∞, by convex polynomials Pn of degree at most n with the accuracy o(n−2/p). This follows from the estimate ∥f−Pn∥p ≤ c · n−2/p·ωφ2(f, n−1)1/q, where 1 ≤ p ≤ ∞, p−1 + q-−1 = 1, φ(x) = (1 − x2)1/2, and ωφ2(f, t) is the Ditzian-Totik modulus of smoothness in the uniform metric
We consider here best approximation by n-convex functions. We first show that if f∈L1[0,1], then the...
Polynomial approximation on convex polytopes in \mathbf{R}^d is considered in uniform and L^p-norms....
AbstractGiven a monotone or convex function on a finite interval we construct splines of arbitrarily...
AbstractA convex function f given on [−1, 1] can be approximated in Lp, 1 < p < ∞, by convex polynom...
AbstractWe prove that for each convex function ƒ ∈ Lp, 0 < p < 1, there exists a convex algebraic po...
AbstractIn this paper we show that the best approximation of a convex function by convex algebraic p...
AbstractIn this paper we show that the best approximation of a convex function by convex algebraic p...
We prove a direct theorem for convex polynomial L p-approximation, 0 < p < 1, in terms of the ...
AbstractWe obtain uniform estimates for monotone and convex approximation of functions by algebraic ...
AbstractWe obtain uniform estimates for monotone and convex approximation of functions by algebraic ...
AbstractLet X = C[0, 1] and let b be the set of continuous convex functions on [0, 1]. If ƒ ϵ X, the...
Let X = C[0, 1] and let b be the set of continuous convex functions on [0, 1]. If ƒ ϵ X, then the se...
Abstract. Let f ∈ C[−1, 1] change its convexity finitely many times in the interval, say s times, at...
Abstract. We prove that a convex function f 2 L p [1; 1], 0 < p < 1, can be approxi-mated by c...
AbstractIf S is a bounded convex subset of Rm, the problem is to find a best approximation to a func...
We consider here best approximation by n-convex functions. We first show that if f∈L1[0,1], then the...
Polynomial approximation on convex polytopes in \mathbf{R}^d is considered in uniform and L^p-norms....
AbstractGiven a monotone or convex function on a finite interval we construct splines of arbitrarily...
AbstractA convex function f given on [−1, 1] can be approximated in Lp, 1 < p < ∞, by convex polynom...
AbstractWe prove that for each convex function ƒ ∈ Lp, 0 < p < 1, there exists a convex algebraic po...
AbstractIn this paper we show that the best approximation of a convex function by convex algebraic p...
AbstractIn this paper we show that the best approximation of a convex function by convex algebraic p...
We prove a direct theorem for convex polynomial L p-approximation, 0 < p < 1, in terms of the ...
AbstractWe obtain uniform estimates for monotone and convex approximation of functions by algebraic ...
AbstractWe obtain uniform estimates for monotone and convex approximation of functions by algebraic ...
AbstractLet X = C[0, 1] and let b be the set of continuous convex functions on [0, 1]. If ƒ ϵ X, the...
Let X = C[0, 1] and let b be the set of continuous convex functions on [0, 1]. If ƒ ϵ X, then the se...
Abstract. Let f ∈ C[−1, 1] change its convexity finitely many times in the interval, say s times, at...
Abstract. We prove that a convex function f 2 L p [1; 1], 0 < p < 1, can be approxi-mated by c...
AbstractIf S is a bounded convex subset of Rm, the problem is to find a best approximation to a func...
We consider here best approximation by n-convex functions. We first show that if f∈L1[0,1], then the...
Polynomial approximation on convex polytopes in \mathbf{R}^d is considered in uniform and L^p-norms....
AbstractGiven a monotone or convex function on a finite interval we construct splines of arbitrarily...
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