Two operators are introduced for the weighted L p approximation on the semiaxis with weight w β (x) = x α exp(−x β ), α > −1/p, 0 < β ≤ 1, allowing a much wider class of functions than in the case of classical Szász–Mirakyan and Butzer operators. It is shown that in case 1/2 < β ≤ 1, only pointwise convergence holds, while for 0 < β ≤ 1/2, direct and converse theorems in terms of a weighted modulus of smoothness hold. Voronǒvskaya-type relations are also proved.
A Weighted Generalization of Szász–Mirakyan and Butzer Operators / DELLA VECCHIA, Biancamaria; Szabados, Jozsef; Mastroianni, Giuseppe. - In: MEDITERRANEAN JOURNAL OF MATHEMATICS. - ISSN 1660-5446. - STAMPA. - 12:2(2014), pp. 433-454. [10.1007/s00009-014-0413-2]
A Weighted Generalization of Szász–Mirakyan and Butzer Operators
DELLA VECCHIA, Biancamaria;
2014
Abstract
Two operators are introduced for the weighted L p approximation on the semiaxis with weight w β (x) = x α exp(−x β ), α > −1/p, 0 < β ≤ 1, allowing a much wider class of functions than in the case of classical Szász–Mirakyan and Butzer operators. It is shown that in case 1/2 < β ≤ 1, only pointwise convergence holds, while for 0 < β ≤ 1/2, direct and converse theorems in terms of a weighted modulus of smoothness hold. Voronǒvskaya-type relations are also proved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
