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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
Authors:
Biancamaria Della Vecchia
,
Giuseppe Mastroianni
, and
Szabados J
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.
Acta Mathematica Hungarica
Authors:
B. Della Vecchia
,
G. Mastroianni
, and
J. Szabados
Abstract
We prove that the weighted error of approximation by the Szász-Mirakyan-type operator introduced in [1] is equivalent to the modulus of smoothness of the function. This result is analogous to previous results for Bernstein-type operators obtained by Ditzian-Ivanov and Szabados.
