@article{Dzyubenko_2017, title={Pointwise estimation of an almost copositive approximation of continuous
functions by algebraic polynomials}, volume={69}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/1723}, abstractNote={In the case where a function continuous on a segment $f$ changes its sign at $s$ points $y_i : 1 < y_s < y_{s-1} < ... < y_1 < 1$,
for any $n \in N$ greater then a constant $N(k, y_i)$ that depends only on $k \in N$ and \$\min_{i=1,...,s-1}\{ y_i - y_{i+1}\}$, we determine
an algebraic polynomial $P_n$ of degree \leq n such that: $P_n$ has the same sign as f everywhere except possibly small neighborhoods of the points $y_i$:
($$(y_i \rho_n(y_i), y_i + \rho_n(y_i)),\quad \rho_n(x) := 1/n2 + \sqrt{1 - x^2}/n,$$
$P_n(y_i) = 0$ and
$$| f(x) P_n(x)| \leq c(k, s)\omega_k(f, \rho_n(x)),\quad x \in [ 1, 1],$$
where $c(k, s)$ is a constant that depends only on $k$ and $s$ and $\omega k(f, \cdot )$ is the modulus of continuity of the function $f$ of
order $k$.}, number={5}, journal={Ukrainsâ€™kyi Matematychnyi Zhurnal}, author={Dzyubenko, H. A.}, year={2017}, month={May}, pages={641-649} }