Konovalov E. O., Chernitska O. V., Atanova M. J.
Oles Honchar Dnipropetrovsk National University
APPLICATION OF KORNIYCHUK 'S INEQUALITY TO THE UPPER BOUND DIMENSIONAL LINEAR WIDTHS
SUBCLASS OF SPACES
(p = 4)
Inequality which is valid for all for
was established and proven by M.P Korniychuk [1, p. 225-226]:
=
. (1)
Inequality is examined for significance . The continuous function f(t),
[а,b] is considered and has the view such as on the drawing (Fig. 1).
Fig. 1. Function f(t)
Function becomes negative in the intervals
. If you want to do the inequality (1) correct, you will require compliance next equality:
. (2)
So, if function f(t) such as on the drawing, for p=4 and , next inequality will correct:
, (3)
where – is the modulus of continuity of function f(t).
The list of references:
1. Korneychuk N. P. Splines in theory of approximations. – M.: Science, Home edition physical and mathematical literature, 1984. – 352 p.