Open AccessNecessary conditions of optimality of quadrature formulas with weight on some classes of differentiable functions
Author(s) -
Ye.Ye. Dunaichuk
Publication year - 1987
Publication title -
researches in mathematics
Language(s) - English
Resource type - Journals
eISSN - 2664-5009
pISSN - 2664-4991
DOI - 10.15421/248708
Subject(s) - quadrature (astronomy) , mathematics , differentiable function , weight function , pure mathematics , mathematical analysis , physics , optics
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 $W^r_p$, $r = 1, 2, \ldots$, $p = 2$, $p = \infty$.