Approximation with an arbitrary order by generalized Kantorovich-type and Durrmeyer-type operators on [0;+\infinit)
DOI:
https://doi.org/10.24193/subbmath.2017.4.07Abstract
Given an arbitrary sequence ¸n > 0, n 2 N, with the prop-
erty that limn!1 ¸n = 0 as fast we want, in this note we introduce
modi¯ed/generalized Sz¶asz-Kantorovich, Baskakov- Kantorovich, Sz¶asz-
Durrmeyer-Stancu and Baskakov-Sz¶asz-Durrmeyer-Stancu operators in
such a way that on each compact subinterval in [0;+1) the order of
uniform approximation is !1(f;
p
¸n). These modi¯ed operators uni-
formly approximate a Lipschitz 1 function, on each compact subinterval
of [0;1) with the arbitrary good order of approximation
p
¸n. The re-
sults obtained are of a de¯nitive character (that is are the best possible)
and also have a strong unifying character, in the sense that for vari-
ous choices of the nodes ¸n, one can recapture previous approximation
results obtained for these operators by other authors.
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