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: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| 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. |
| format | Article |
| id | doaj-art-7d26bdcc2925458e98cef642d7528290 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| 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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