A remark concerning the modulus of smoothness introduced by Ditzian and Totik

Authors

  • O. Yu. Dyuzhenkova

Abstract

For each functionf(x) continuous on the segment [−1, 1], we set ˜f(t)=f(cost) . We study the relationship between the ordinarykth modulus of continuity ωk(τ,˜f(r)) of therth derivative ˜f(r) of the function ˜f and thekth modulus of continuity ˉωk,r(τ,f(r)) with weight ϕ r of the rth derivativef (r) of the functionf introduced by Ditzian and Totik. Thus, ifr is odd andk is even, we prove that these moduli are equivalent ast→0.

Published

25.12.1995

Issue

Section

Research articles

How to Cite

Dyuzhenkova, O. Yu. “A Remark Concerning the Modulus of Smoothness Introduced by Ditzian and Totik”. Ukrains’kyi Matematychnyi Zhurnal, vol. 47, no. 12, Dec. 1995, pp. 1627–1638, https://umj.imath.kiev.ua/index.php/umj/article/view/5556.