Author:
Leviatan D.,Motorna O. V.,Shevchuk I. A.
Abstract
UDC 517.5
We say that a function
f
∈
C
[
a
,
b
]
is
q
-monotone,
q
≥
3
, if
f
∈
C
q
-
2
(
a
,
b
)
and
f
(
q
-
2
)
is convex in
(
a
,
b
)
. Let
f
be continuous and
2
π
-periodic, and change its
q
-monotonicity finitely many times in
[
-
π
,
π
]
. We are interested in estimating the degree of approximation of
f
by trigonometric polynomials which are co-
q
-monotone with it, namely, trigonometric polynomials that change their
q
-monotonicity exactly at the points where
f
does. Such Jackson type estimates are valid for piecewise monotone (
q
=
1
) and piecewise convex (
q
=
2
) approximations. However, we prove, that no such estimates are valid, in general, for co-
q
-monotone approximation, when
q
≥
3
.
Publisher
Institute of Mathematics National Academy of Sciences of Ukraine
Subject
General Earth and Planetary Sciences,General Engineering,General Environmental Science
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