ON FUNCTIONAL EQUATIONS CONNECTED WITH QUADRATURE RULES

被引：0

作者：

Koclega-Kulpa, Barbara ^{[1
]}

Szostok, Tomasz ^{[1
]}

Wasowicz, Szymon ^{[2
]}

机构：

[1] Silesian Univ, Inst Math, PL-40007 Katowice, Poland

[2] Univ Bielsko Biala, Dept Math & Comp Sci, PL-43309 Bielsko Biala, Poland

来源：

GEORGIAN MATHEMATICAL JOURNAL | 2009年 / 16卷 / 04期

关键词：

Approximate integration; functional equations; polynomial functions; quadrature rules;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The functional equations of the form F(y) - F(x) = (y-x)[alpha(0)f(x) + Sigma(n)(k=1)alpha(k)f(lambda(k)x + (1 - lambda(k))y) + alpha(n+1)f(y)] are considered. They are connected with quadrature rules of the approximate integration. We show that such equations characterize polynomials in the class of continuous functions. It is also shown that if the number of components is sufficiently small, then the continuity is forced by the equation itself. Unique solvability of the considered problem are established.

引用

页码：725 / 736

页数：12

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