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.

Weighted approximation of functions by Szasz-Myrakyan-type operators

MASTROIANNI, Giuseppe Maria;
2006-01-01

Abstract

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.
2006
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11563/1233
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