| Annotation |
The article discusses several issues related to the task of finding the constants
A[m](k1,...,km)
H = limn→∞nsup
M
[
m](k1,...,km)
n (f, x) − f(x)
, , where M[m](k1,...,km)
n are
trigonometric operators of Baskakov. The constants A[m](k1,...,km)
n are called the exact
constants. The article provides an overview of the results obtained earlier by the authors,
full proofs of results that were previously announced. We give a complete solution of the
problem, as well as m = 1, 2, 3, as well as m = 4,if (k1, k2, k3, k4) = (1, 2, 3, 4), (k1, k2, k3, k4) =
(1, 2, 3, 5), (k1, k2, k3, k4) = (1, 2, 4, 5), п as m = 5, (k1, k2, k3, k4, k5) = (1, 2, 3, 4, 5). We also
investigate the dynamics of change in value of the constant A[1](k)
H the growth parameter k.
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