The authors investigate the approximation of bounded functions with discontinuities of the first kind by generalized Shepard operators. Estimate for the rate of convergence at a continuity point is obtained, while at the points of discontinuity it is shown that the sequence of generalized Shepard operators is almost always divergent. It is also shown that the sequence of Cesaro means of generalized Shepard operators is convergent everywhere for bounded functions which have only discontinuities of the first kind in [0, 1].
On the approximation of bounded functions with discontinuities of the first kind by generalized Shepard operators / R., Bojanic; DELLA VECCHIA, Biancamaria; G., Mastroianni. - In: ACTA MATHEMATICA HUNGARICA. - ISSN 0236-5294. - STAMPA. - 85:(1999), pp. 29-57. [10.1023/a:1006612727274]
On the approximation of bounded functions with discontinuities of the first kind by generalized Shepard operators
DELLA VECCHIA, Biancamaria;
1999
Abstract
The authors investigate the approximation of bounded functions with discontinuities of the first kind by generalized Shepard operators. Estimate for the rate of convergence at a continuity point is obtained, while at the points of discontinuity it is shown that the sequence of generalized Shepard operators is almost always divergent. It is also shown that the sequence of Cesaro means of generalized Shepard operators is convergent everywhere for bounded functions which have only discontinuities of the first kind in [0, 1].I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
