Necessary conditions of optimality of quadrature formulas with weight on some classes of differentiable functions

Ye.Ye. Dunaichuk (Dnipropetrovsk State University)


For the quadrature formula (with positive, continuous weight function) that is defined by the values of the function and its derivatives of up to and including $$$(r-1)$$$-th order, we find necessary conditions of optimality on the classes $$$W^r_p$$$, $$$r = 1, 2, \ldots$$$, $$$p = 2$$$, $$$p = \infty$$$.


Lebed' G.K. "On quadrature formulas with the smallest estimate of remainder on some classes of functions", Izv. AN SSSR. Ser. Matem., 1970; 3(4): pp. 645-669. (in Russian) doi:10.1070/IM1970v004n03ABEH000925




  • There are currently no refbacks.

Copyright (c) 1987 Ye.Ye. Dunaichuk

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Registered in

ISSN (Online): 2664-5009
ISSN (Print): 2664-4991