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Weighted approximation of functions by Szász--Mirakyan-type operators |
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| Authors: | Biancamaria Della Vecchia Giuseppe Mastroianni Szabados J |
| Institution: | (1) Dipartimento di Matematica, Universitá di Roma ``La Sapienza', Piazzale Aldo Moro 2, I-00185 Roma, Italy;(2) Dipartimento di Matematica, Universitá della Basilicata, Contrada Macchia Romana, I-85100 Potenza, Italy;(3) Alfréd Rényi Institute of Mathematics, H-1364 Budapest, P.O.B. 127, Hungary |
| Abstract: | 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. |
| Keywords: | weighted modulus of smoothness Szász--Mirakyan operator direct and converse results |
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