Approximation of curves by broken lines in Lp

Abstract

In this paper was found the exact values of upper bounds deviation in Lp[0,L] (1 6 p < ∞) metrics of curve 􀀀, defined by parametric equations in n-dimensional space of inscribed in its at the points tk = kL/N, k = 0,N a broken line on the H!1,...,!m class given both as an arbitrary or convex modulus of continuity !i(t), i = 1,m. The problem of finding the upper bounds of deviation of parametric given curves 􀀀,G ∈ H!1,!2,...,!m coordinate functions 'i(t) and i(t) (i = 1,m) of which respectively belong to the class H!i [0,L] (i = 1,m) intersect in N (N ≥ 2) points of the partition to the segment [0,L]. The obtained results are generalizations of the result of V. F. Storchai on the approximation of continuous functions by interpolation polygonal lines in the metric of the space Lp[0,L] (1 ≤ p ≤ ∞). Refs 16.