On the approximation of bounded functions with discontinuities of the first kind by generalized Shepard operators

被引：3

作者：

Bojanic, R

Della Vecchia, B

Mastroianni, G

机构：

[1] Ohio State Univ, Dept Math, Columbus, OH 43210 USA

[2] Univ Rome La Sapienza, Dipartimento Matemat, I-00185 Rome, Italy

[3] Univ Basilicata, Dipartimento Matemat, I-85100 Potenza, Italy

来源：

ACTA MATHEMATICA HUNGARICA | 1999年 / 85卷 / 1-2期

关键词：

Bounded Function; Continuity Point; Shepard Operator;

D O I：

10.1023/A:1006612727274

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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].

引用

页码：29 / 57

页数：29

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