Abstract:
We consider the approximation of a special class of complex functions
f that is analytic on the disk
\textU = \left\ z \in \rmC:\dfrac12 < \left| z \right| < 1 \right\ , whose origin is its essential singularity. We obtain the exact Jackson inequality between the best approximation
E_n - 1\left( f \right)_2 of functions
f and
m-order continuous modules of functions
z^rf^\left( r \right) . We also obtain the exact Jackson inequality between the best approximation
E_n - 1\left( f \right)_2 of function
f and
\calK -functional. Then we obtain the exact Jackson inequality between the best approximation
E_n - 1\left( f \right)_2 of functions
f and weighted integral of
m-order continuous modules of functions
z^rf^\left( r \right) . Finally, we obtain the best approximation and n-widths in the functions classes of
m-order continuous modules of functions
z^rf^\left( r \right) , in the functions classes of weighted integral of
m-order continuous modules of functions
z^rf^\left( r \right) and in the functions classes of
\calK -functional respectively.