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.