Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Jackson's type estimate of nearly coconvex approximation   Suppose that a continuous on the real axis $2\pi$-periodic function $f$
changes its convexity at $2s,\ s\in\Bbb N,$ points $y_i$ on each period:
$-\pi\le y_{2s}<y_{2s-1}<...<y_1<\pi,$ and for the rest $i\in\Bbb Z,$ the
points $y_i$ are defined periodically. In the paper, for each $n\ge N,$ a
trigonometric polynomial $P_n$ of order $cn$ is found such that: $P_n$ has the
same convexity as $f,$ everywhere except, perhaps, the small neighborhoods of
the $y_i:$ $$ (y_i-\pi/n,y_i+\pi/n) $$ and $$ \|f-P_n\|\le
c(s)\,\omega_4(f,\pi/n), $$ where $N$ is a constant depending only on
$\min\limits_{i=1,...,2s}\{y_i-y_{i+1}\},\ c$ and $c(s)$ are constants
depending only on $s,\ \omega_4(f,\cdot)$ is the modulus of continuity of the
$4$-th order of the function $f,$ and $\|\cdot\|$ is the max-norm.

18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio