Approximating the Stieltjes integral via a weighted trapezoidal rule with applications

被引：2

作者：

Dragomir, S. S. ^{[1
,2
]}

Fedotov, I. ^{[3
]}

机构：

[1] Victoria Univ, Sch Sci & Engn, Melbourne, Vic 8001, Australia

[2] Univ Witwatersrand, Sch Computat & Appl Math, ZA-2050 Johannesburg, South Africa

[3] Tshwane Univ Technol, Dept Math & Stat, ZA-001 Pretoria, South Africa

来源：

MATHEMATICAL AND COMPUTER MODELLING | 2013年 / 57卷 / 3-4期

关键词：

Stieltjes integral; Riemann integral; Generalized trapezoid inequality; Selfadjoint operators; Functions of selfadjoint operators; Spectral representation; OSTROWSKI TYPE INEQUALITIES; GRUSS INEQUALITY; MAPPINGS;

D O I：

10.1016/j.mcm.2012.07.023

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

In this paper we provide sharp error bounds in approximating the weighted Riemann-Stieltjes integral integral(b)(a)f(t)g(t)d alpha(t) by the weighted trapezoidal rule f(a)+f(b)/2 integral(b)(a)g(t) d alpha(t). Applications for continuous functions of selfadjoint operators in complex Hilbert spaces are given as well. (C) 2012 Elsevier Ltd. All rights reserved.

引用

页码：602 / 611

页数：10

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