Geodesic
A family of operators with discontinuous ranges and approximation and restoration of continuous functions
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 10, pp. 1603-1609 
A. P. Khromov; G. V. Khromova. A family of operators with discontinuous ranges and approximation and restoration of continuous functions. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 10, pp. 1603-1609. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_10_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A class of operators whose construction is similar to but simpler than the construction of Landau operators is the basis for the design of a modified family of operators with discontinuous ranges. This family has good approximation properties with respect to approximation and restoration problems for continuous functions.

[1] Goncharov V. L., Teoriya interpolirovaniya i priblizheniya funktsii, GITL, M., 1954

[2] Khromov A. P., Khromova G. V., “Ob odnoi modifikatsii operatora Steklova”, Sovremennye problemy teorii funktsii i ikh prilozheniya, Tez. dokl. 15-i Sarat. zim. shkoly, Izd-vo Sarat. un-ta, Saratov, 2010

[3] Khromova G. V., “O zadache vosstanovleniya funktsii, zadannykh s pogreshnostyu”, Zh. vychisl. matem. i matem. fiz., 17:5 (1977), 1161–1171 | MR | Zbl

[4] Ivanov V. K., Vasin V. V., Tanana V. P., Teoriya lineinykh nekorrektnykh zadach i ee prilozheniya, Nauka, M., 1978 | MR

[5] Khromova G. V., “Ob otsenkakh pogreshnosti priblizhennykh reshenii uravnenii pervogo roda”, Dokl. AN, 378:5 (2001), 605–609 | MR | Zbl