Abstract
In this paper we show that for $f$ continuous on $[ - 1, + 1]$ and satisfying $(f({x_2}) - f({x_1}))/({x_2} - {x_1}) \geqq \delta > 0$, it is possible to have infinitely many of the polynomials of best uniform approximation to $f$ not increasing on $[ - 1, + 1]$.
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