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  • 1 Dipartimento di Matematica, Universitá di Roma ``La Sapienza'' Piazzale Aldo Moro 2, I-00185 Roma, Italy Piazzale Aldo Moro 2, I-00185 Roma, Italy
  • 2 Dipartimento di Matematica, Universitá della Basilicata Contrada Macchia Romana, I-85100 Potenza, Italy Contrada Macchia Romana, I-85100 Potenza, Italy
  • 3 Alfréd Rényi Institute of Mathematics H-1364 Budapest, P.O.B. 127, Hungary H-1364 Budapest, P.O.B. 127, Hungary
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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.

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