TY - JOUR
AU - V. F. Babenko
AU - S. V. Konareva
PY - 2018/09/25
Y2 - 2024/07/25
TI - Jackson – Stechkin-type inequalities for the approximation of elements of Hilbert spaces
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 70
IS - 9
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/1626
AB - We introduce new characteristics for elements of Hilbert spaces, namely, generalized moduli of continuity \$\omega_{ \varphi} (x, L_p, V ([0, \delta]))$ and obtain new exact Jackson – Stechkin-type inequalities with these moduli of continuity for the approximation ofelements of Hilbert spaces. These results include numerous well-known inequalities for the approximation of periodic functions by trigonometric polynomials, approximation of nonperiodic functions by entire functions of exponential type, similar results for almost periodic functions, etc. Some of these results are new even in these classical cases.
ER -