Exact constants in inequalities of the jackson type for quadrature formulas - Doronin, V. G.; Ligun, A. A. (Ukrains’kyi Matematychnyi Zhurnal, 2000)
We prove that if \(R_n ( f,{ t_k } ,{ p_k } )\) 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: \(_{ f_k } ,{ p_k } _f L_1^r R_1 | R_n (f,{ t_k } ,{ p_k } ) | ω (f^(r) ,δ )_1 = π \| D_1 \|_∞ n^r \) whereD r is the Bernoulli kernel.