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- Author or Editor: Giuseppe Mastroianni x
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Weighted approximation of functions by Szász--Mirakyan-type operators
Sz\'asz--Mirakyan operator, weighted modulus of smoothness, direct and converse results
Summary
We give error estimates for the weighted approximation of functions with singularities at the endpoints on the semiaxis by some modifications of Sz\'asz--Mirakyan operators. To do so, we define a new weighted modulus of smoothness and prove its equivalence to the weighted K-functional. Also, the class of functions for which the modified Sz\'asz--Mirakyan operator can be defined will be extended to a much wider set than for the original operator.
The authors investigate two sets of nodes for bivariate Lagrange interpolation in [−1, 1] 2 and prove that the order of the corresponding Lebesgue constants is (log n ) 2 .
Abstract
We give direct and converse results for the weighted approximation of functions with endpoint or inner singularities by Bernstein operators.
