For all odd r we construct a linear operator Br,r(f) which maps the set of 2π-periodic functionsf(t)ε X(r) (X(r)=C(r) or L1(r)) into a set of trigonometric polynomials of order not higher than n-1… Expand

We establish exact inequalities for the upper bounds of seminorms on classes of differentiable periodic functions, and as corollaries of them, exact inequalities between the best approximations by… Expand

In this note inequalities between the norms of a spline and its derivatives in various Orlich spaces are obtained. These inequalities are analogs of the inequalities of L. V. Takov for… Expand

We present a description of convex curves, which enables one to reduce the problem of approximation of a convex curve by piecewise circular lines in the Hausdorff metric to the problem of… Expand

AbstractA polyhedral functionlp(Δn) (f). interpolating a function f, defined on a polygon Φ, is defined by a set of interpolating nodes Δn ⊂Φ and a partition P(Δn) of the polygon Φ into triangles… Expand