Access the full text.
Sign up today, get DeepDyve free for 14 days.
N. Barnett, S. Dragomir (1998)
AN OSTROWSKI TYPE INEQUALITY FOR DOUBLE INTEGRALS AND APPLICATIONS FOR CUBATURE FORMULAE
D. Mitrinovic, J. Pečarić, A. Fink (1992)
Classical and New Inequalities in Analysis
S. Dragomir, P. Cerone, N. Barnett, J. Roumeliotis (1999)
An Inequality of the Ostrowski Type For Double Integrals and Applications for Cubature Formulae
B. Pachpatte (2002)
On Grüss Type Inequalities for Double IntegralsJournal of Mathematical Analysis and Applications, 267
(1882)
Sue les expressions approximatives des intégrales definies parles aures prises entre les mêmes limites
(1999)
N
DEMONSTRATIO MATHEMATICAVol. XLNo 12007B. G. PachpatteNEW INEQUALITIES OF CEBYSEV TYPEFOR DOUBLE INTEGRALSAbstract. In this paper, we establish new inequalities of Cebysev t y p e involvingfunctions of two independent variables by using certain integral identities.1. IntroductionIn 1882, P. L. Cebysev [2] proved the following classical inequality6(1.1)j f(x)g(x)dxa/ - . b-(^\$f(x)dxa/ibj f\ g(x)d:X) — a J"" '' \aprovided / , g are absolutely continuous functions defined on [a, 6] and / ' , g' €Loo [a, b].Since the publication of [2], a number of researchers have given variousgeneralizations, extensions and variants of the above inequality, see [4] andalso some of the recent papers appeared in RGMIA Research Report Collection. The main purpose of this paper is to establish new inequalities similarto the inequality (1.1), involving functions of two independent variables andtheir partial derivatives and double integrals. The analysis used in the proofsis based on the integral identities proved in [1] and [3].2. Statement of resultsLet R denotes the set of real numbers and A = [a, b] x [c, d], a, b, c, dG R. The partial derivatives of a function z(x, y) defined on A are denoted by Diz{x,y)= J^z(x,y),D2z(x,y)= J^z(x,y),D2Diz{x,y)=(x, y). We denote by C (A) the class
Demonstratio Mathematica – de Gruyter
Published: Jan 1, 2007
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.