Exact constants in inequalities of the jackson type for quadrature formulas

• Date: 2000
• Main Authors: Doronin, V. G., Ligun, A. A., Доронин, В. Г., Лигун, А. А.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2000
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4395
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We prove that if \(R_n \left( {f,\{ t_k \} ,\{ p_k \} } \right)\) is the error of a simple quadrature formula and ω(ε, δ)1 is the integral modulus of continuity, then, for any δ ≥/π andn,r = 1, 2, …, the following equality is true: \(\mathop {\inf }\limits_{\{ f_k \} ,\{ p_k \} } \mathop {\sup }...