ANZIAM  J.  46 (2005), 555-574

Sharp integral inequalities based on general Euler two-point formulae

J. Pecaric   Faculty of Textile Technology   University of Zagreb   Pierottijeva 6   10000 Zagreb   Croatia     pecaric@mahazu.hazu.hr I. Peric   Faculty of Food Technology and Biotechnology   Mathematics Department   University of Zagreb   Pierottijeva 6   10000 Zagreb   Croatia   iperic@pbf.hr and A. Vukelic   Faculty of Food Technology and Biotechnology   Mathematics Department   University of Zagreb   Pierottijeva 6   10000 Zagreb   Croatia   avukelic@pbf.hr

Abstract

We consider a family of two-point quadrature formulae, using some Euler-type identities. A number of inequalities, for functions whose derivatives are either functions of bounded variation, Lipschitzian functions or R-integrable functions, are proved.

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