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