臺灣博碩士論文加值系統

我們提出一個Gruess型態積分不等式，它是建立在兩個分別為遞增型態與r-Hoelder型態之函數上，並提出遞增型態之函數在擾動梯形公式與類梯形公式之數值積分上的應用例子。

We give an integral inequality of Gruess'' type for two mappings of increasing type and of r-Hoelder''s type. We also provide the applications for perturbed trapezoid formula and quasi-trapezoid formula and examples in numerical integration.

1. Introduction 1
2. Main Theory 3
3. Application for Trapezoid Formula 5
References 13

[1] Xiao-Liang Cheng and Jie Sun, A Note on The Perturbed Trapezoid Inequality, Journal of Inequalities in Pure and Applied Mathematics,3(2), Article 29, 2002.
[2] Sever Silvestru Dragomir, A Gruess'' Type Inequality for Mappings of r-Hoelder''s Type and Applications for Trapezoid Formula, Tamkang Journal of Mathematics, 31(1), 2000, pp. 43-47.
[3] Dragoslav S. Mitrinovic, J. E. Pecaric and A.M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic Publishers, Dordrecht, 1993.
[4] Gerhard Gruess, Über das Maximum des absoluten Betrages von 1/((b-a)) ∫_a^b▒〖f(x)g(x)dx〗-1/〖(b-a)〗^2 ∫_a^b▒〖f(x)dx〗 ∫_a^b▒〖g(x)dx〗, Mathematische Zeitschrift, 39(1), 1935, pp. 215–226.
[5] Zheng Liu, Some inequalities of perturbed trapezoid type, Journal of Inequalities in Pure and Applied Mathematics, 7(2), Article 47, 2006.

[6] Sever Silvestru Dragomir, P. Cerone and A. Sofo, Some remarks on the trapezoid rule in numerical integration, Indian Journal Pure and Applied Mathematics, 31(5), 2000, pp. 475-494.

[7] Xiao-Liang Chengm, Improvement od some Ostrowski-Gruess type inequalities, Computers Mathematics applications, 42, 2001, pp. 109--114.

[8] Sever Silvestru Dragomir and S. Wang, An inequality of Ostrowski-Gruess'' type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rules, Computers Mathematics applications, 33(11), 1997, pp. 15-20.

[9] M. Matic, J. Pecaric and N. Ujevic, Improvement and further generalization of inequalities of Ostrowski-Gruess type, Computers Mathematics applications, 39(3-4), 2000, pp. 161-175.