Sharp Integral Inequalities Based on a General Four-Point Quadrature Formula via a Generalization of the Montgomery Identity

We consider families of general four-point quadrature formulae using a generalization of the Montgomery identity via Taylor’s formula. The results are applied to obtain some sharp inequalities for functions whose derivatives belong to 𝐿𝑝 spaces. Generalizations of Simpson’s 3/8 formula and the Lobat...

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Main Authors: J. Pečarić, M. Ribičić Penava
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2012/343191
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author J. Pečarić
M. Ribičić Penava
author_facet J. Pečarić
M. Ribičić Penava
author_sort J. Pečarić
collection DOAJ
description We consider families of general four-point quadrature formulae using a generalization of the Montgomery identity via Taylor’s formula. The results are applied to obtain some sharp inequalities for functions whose derivatives belong to 𝐿𝑝 spaces. Generalizations of Simpson’s 3/8 formula and the Lobatto four-point formula with related inequalities are considered as special cases.
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series International Journal of Mathematics and Mathematical Sciences
spelling doaj-art-7d26bdcc2925458e98cef642d75282902025-08-20T03:35:28ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/343191343191Sharp Integral Inequalities Based on a General Four-Point Quadrature Formula via a Generalization of the Montgomery IdentityJ. Pečarić0M. Ribičić Penava1Faculty of Textile Technology, University of Zagreb, Pierottijeva 6, 10000 Zagreb, CroatiaDepartment of Mathematics, University of Osijek, Trg Ljudevita Gaja 6, 31 000 Osijek, CroatiaWe consider families of general four-point quadrature formulae using a generalization of the Montgomery identity via Taylor’s formula. The results are applied to obtain some sharp inequalities for functions whose derivatives belong to 𝐿𝑝 spaces. Generalizations of Simpson’s 3/8 formula and the Lobatto four-point formula with related inequalities are considered as special cases.http://dx.doi.org/10.1155/2012/343191
spellingShingle J. Pečarić
M. Ribičić Penava
Sharp Integral Inequalities Based on a General Four-Point Quadrature Formula via a Generalization of the Montgomery Identity
International Journal of Mathematics and Mathematical Sciences
title Sharp Integral Inequalities Based on a General Four-Point Quadrature Formula via a Generalization of the Montgomery Identity
title_full Sharp Integral Inequalities Based on a General Four-Point Quadrature Formula via a Generalization of the Montgomery Identity
title_fullStr Sharp Integral Inequalities Based on a General Four-Point Quadrature Formula via a Generalization of the Montgomery Identity
title_full_unstemmed Sharp Integral Inequalities Based on a General Four-Point Quadrature Formula via a Generalization of the Montgomery Identity
title_short Sharp Integral Inequalities Based on a General Four-Point Quadrature Formula via a Generalization of the Montgomery Identity
title_sort sharp integral inequalities based on a general four point quadrature formula via a generalization of the montgomery identity
url http://dx.doi.org/10.1155/2012/343191
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AT mribicicpenava sharpintegralinequalitiesbasedonageneralfourpointquadratureformulaviaageneralizationofthemontgomeryidentity