ANZIAM  J.  44 (2003), 355-364

A quasi-trapezoid inequality for double integrals

N. S. Barnett   School of Communications and Informatics   Victoria University of Technology   PO Box 14428   Melbourne City MC, VIC 8001   Australia     neil@matilda.vu.edu.au S. S. Dragomir   School of Communications and Informatics   Victoria University of Technology   PO Box 14428   Melbourne City MC, VIC 8001   Australia     sever@matilda.vu.edu.au and C. E. M. Pearce   Department of Applied Mathematics   The University of Adelaide   Adelaide SA 5005   Australia   cpearce@maths.adelaide.edu.au

Abstract

A quasi-trapezoid inequality is derived for double integrals that strengthens considerably existing results. A consonant version of the Grüss inequality is also derived. Applications are made to cubature formulae and the error variance of a stationary variogram.

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