Abstract:
In this paper we find sharp inequalities of Jackson-Stechkin type
between the best approximations of periodic differentiable functions
by trigonometric polynomials and generalized moduli of continuity of
$m$-th order in the space $L_{2}.$ The exact values of various
$n$-widths of classes of functions from $L_{2}$ defined by the
generalized modus of continuity of the $r$-th derivative of the
function f are calculated.
Key words:best approximation, trigonometric polynomials, generalized
modulus of continuity of higher order, $n$-widths.
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