Exact constants in inequalities of the jackson type for quadrature formulas
Abstract
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: \(\mathop {\inf }\limits_{\{ f_k \} ,\{ p_k \} } \mathop {\sup }\limits_{f \in L_1^r \backslash R_1 } \frac{{\left| {R_n (f,\{ t_k \} ,\{ p_k \} )} \right|}}{{\omega (f^{(r)} ,\delta )_1 }} = \frac{{\pi \left\| {D_1 } \right\|_\infty }}{{n^r }}\) whereD r is the Bernoulli kernel.Downloads
Published
25.01.2000
Issue
Section
Research articles
How to Cite
Doronin, V. G., and A. A. Ligun. “Exact Constants in Inequalities of the Jackson Type for Quadrature Formulas”. Ukrains’kyi Matematychnyi Zhurnal, vol. 52, no. 1, Jan. 2000, pp. 46-51, https://umj.imath.kiev.ua/index.php/umj/article/view/4395.