THE BEST APPROXIMATION CONSTANT FOR THE JACKSON'S TYPE OPERATOR J_(n,3) (f;x)

In this paper we obtain the best approximation constant of function f(x)(∈C_(2π))by theJackson's type operator J_(π3)(f;x),i.e.‖J_(n,3)(f,x)-f(x)‖_c≤(4-6/π)ω(f,1/n),‖J_(n,3)(f,x)-f(x)‖_c≤(8-17/π)ω_2(f,1/n)

The best approximation constant for the Jackson’s type operator Jn,3(f;x)

In this paper we obtain the best approximation constant of function f(x) (∈C_2π) by the Jackson’s type operator J_n,3(f; x), i.e. $$\begin{gathered} \left\| {J_{n,3} \left( {f,x} \right) - f\left( x \right)} \right\|_c \leqslant \left( {4 - \frac{6}{\pi }} \right)\omega \left( {f - \frac{1}{n}} \right), \hfill \\ \left\| {J_{n,3} \left( {f,x} \right) - f\left( x \right)} \right\|_c \leqslant \left( {8 - \frac{{17}}{\pi }} \right)\omega _2 \left( {f - \frac{1}{n}} \right) \hfill \\ \end{gathered} $$ .