TY - JOUR

T1 - Sharp Jackson type inequalities for spline approximation on the axis

AU - Gladkaya, A. V.

AU - Vinogradov, O. L.

PY - 2017/3/1

Y1 - 2017/3/1

N2 - We establish several Jackson type inequalities with explicit constants for spline approximation of functions defined on the real axis. The inequalities for the first modulus of continuity of odd derivatives are sharp. We also obtain inequalities for high-order moduli of continuity of a function itself. One of the inequalities for the second modulus of continuity is sharp. Up to the present paper no estimates for spline approximation on the axis in terms of high-order moduli of continuity, with constants written explicitly, were known.

AB - We establish several Jackson type inequalities with explicit constants for spline approximation of functions defined on the real axis. The inequalities for the first modulus of continuity of odd derivatives are sharp. We also obtain inequalities for high-order moduli of continuity of a function itself. One of the inequalities for the second modulus of continuity is sharp. Up to the present paper no estimates for spline approximation on the axis in terms of high-order moduli of continuity, with constants written explicitly, were known.

KW - Akhiezer–Krein–Favard type operator

KW - Jackson type inequality

KW - modulus of continuity

KW - spline

UR - http://www.scopus.com/inward/record.url?scp=85013904603&partnerID=8YFLogxK

U2 - 10.1007/s10476-017-0102-z

DO - 10.1007/s10476-017-0102-z

M3 - Article

AN - SCOPUS:85013904603

VL - 43

SP - 27

EP - 47

JO - Analysis Mathematica

JF - Analysis Mathematica

SN - 0133-3852

IS - 1

ER -