Abstract
Abstract
Let sequences
,
satisfy the relations
,
,
,
as
, and let
and
. We redefine the function
as
on the interval
by polygonal arcs in such a way that the function remains continuous and vanishes on a neighbourhood of the ends of the interval. Also let the function
and the pair of sequences
,
be connected by the equiconvergence condition. Then for the classical Lagrange–Jacobi interpolation processes
to approximate
uniformly with respect to
on
it is sufficient that
have bounded variation
on
. In particular, if the sequences
and
are bounded, then for the classical Lagrange–Jacobi interpolation processes
to approximate
uniformly with respect to
on
it is sufficient that the variation of
be bounded on
,
.
Cited by
2 articles.
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