Exact constants in inequalities of the jackson type for quadrature formulas

  • V. G. Doronin
  • A. A. Ligun


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.
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.
Research articles