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arXiv 1901.01147math.CA
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误差估计为Lp的黎曼-斯蒂尔切斯积分的两点Quadrature规则

Two-Point Quadrature Rules for Riemann-Stieltjes Integrals with Lp-error estimates

Mohammad W. Alomari

备注：
19 pages. arXiv admin note: text overlap with arXiv:1812.10674
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摘要：

本文对黎曼-斯蒂尔切斯积分$\int_a^b {f\left( t \right)du\left( t \right)}$构造了一个新的一般两点求积规则，其中被积函数$f$在$[a,b]$上满足赫尔德条件，积分函数$u$在$[a,b]$上有界变差.在相同的假设条件下，证明了对偶公式。文中还给出了一些尖锐误差$L^p$ --对所提出的求积规则的误差估计。

英文摘要：

In this work, we construct a new general two-point quadratre rules for the Riemann--Stieltjes integral $\int_a^b {f\left( t \right)du\left( t \right)}$, where the integrand $f$ is assumed to be satisfied with the Hölder condition on $[a,b]$ and the integrator $u$ is of bounded variation on $[a,b]$. The dual formulas under the same assumption are proved. Some sharp error $L^p$--Error estimates for the proposed quadrature rules are also obtained.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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