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.File in questo prodotto:
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