| Abstract: | For a given nonincreasing vanishing sequence {a
n
}
n = 0
of nonnegative real numbers, we find necessary and sufficient conditions for a sequence {n
k
}
k = 0
to have the property that for this sequence there exists a function f continuous on the interval 0,1] and satisfying the condition that
, k = 0,1,2,..., where E
n
(f) and R
n,m
(f) are the best uniform approximations to the function f by polynomials whose degree does not exceed n and by rational functions of the form r
n,m
(x) = p
n
(x)/q
m
(x), respectively. |
