Taylor-Widder representation formulae and Ostrowski, Gruss, integral means and Csiszar type inequalities

被引：6

作者：

Anastassiou, George A. ^{[1
]}

机构：

[1] Univ Memphis, Dept Math Sci, Memphis, TN 38152 USA

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2007年 / 54卷 / 01期

关键词：

Taylor-Widder formula; representation formulae; Ostrowski and Gruss inequalities; comparison of means; Csiszar f-divergence;

D O I：

10.1016/j.camwa.2006.09.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Based on the very general Taylor-Widder formula, several representation formulae are developed. By applying these are developed very general inequalities of types: Ostrowski, Gruss, comparison of means, Csiszar f-divergence. The estimates involve L-p norms, any I <= p <= infinity. (C) 2007 Elsevier Ltd. All fights reserved.

引用

页码：9 / 23

页数：15

共 8 条

[1] ANASTASSIOU GA, 2006, J INEQUALITIES PURE, V7
[2] Csiszar I., 1967, STUD SCI MATH HUNG, V2, P299
[3] Draghici S., 2000, INEQUALITIES CSISZAR, P1
[4] FINK AM, 1992, CZECH MATH J, V42, P289
[5] On the maximum absolute total of 1/b-a (a)integral(b) f(x)g(x)dx-1/(b-a)(2) (a)integral(b) f(x)dx (a)integral(b) g(x)dx.
Gruss, G
[J]. MATHEMATISCHE ZEITSCHRIFT, 1935, 39 : 215 - 226
[6] Karlin S., 1966, TCHEBYCHEFF SYSTEMS
[7] Ostrowski A., 1937, Comment. Math. Helv, V10, P226, DOI [10.1134/S0001434610010049, DOI 10.1134/S0001434610010049, 10.1007/BF01214290, DOI 10.1007/BF01214290]
[8] A generalization of Taylor's series
Widder, D. V.
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1928, 30 (1-4) : 126 - 154

← 1 →