Some Grüss type inequalities and corrected three-point quadrature formulae of Euler type
We obtain some new Grüss type inequalities for the general corrected three-point quadrature formulae of Euler type. As special cases, we derive some new bounds for the corrected Euler Simpson formula, the corrected dual Euler Simpson formula and the corrected Euler Maclaurin formula. Also, applicati...
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| Published in | Journal of inequalities and applications Vol. 2015; no. 1; p. 1 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Cham
Springer International Publishing
03.03.2015
Springer Nature B.V |
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| Abstract | We obtain some new Grüss type inequalities for the general corrected three-point quadrature formulae of Euler type. As special cases, we derive some new bounds for the corrected Euler Simpson formula, the corrected dual Euler Simpson formula and the corrected Euler Maclaurin formula. Also, applications for the corrected Euler Bullen-Simpson formula are considered. |
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| AbstractList | We obtain some new Grüss type inequalities for the general corrected three-point quadrature formulae of Euler type. As special cases, we derive some new bounds for the corrected Euler Simpson formula, the corrected dual Euler Simpson formula and the corrected Euler Maclaurin formula. Also, applications for the corrected Euler Bullen-Simpson formula are considered. |
| ArticleNumber | 76 |
| Author | Pečarić, Josip Klaričić Bakula, Milica Ribičić Penava, Mihaela Vukelić, Ana |
| Author_xml | – sequence: 1 givenname: Milica surname: Klaricic Bakula fullname: Klaricic Bakula, Milica – sequence: 2 givenname: Josip surname: Pecaric fullname: Pecaric, Josip – sequence: 3 givenname: Mihaela surname: Ribicic Penava fullname: Ribicic Penava, Mihaela – sequence: 4 givenname: Ana surname: Vukelic fullname: Vukelic, Ana |
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| Cites_doi | 10.7153/jmi-08-10 10.7153/jmi-03-54 10.1155/JIA.2005.277 10.1006/jmaa.2000.6977 10.1007/978-94-017-1043-5 10.1016/S0898-1221(00)00324-2 10.1216/rmjm/1181069660 10.1016/j.mcm.2006.05.009 |
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| Copyright | Klaričić Bakula et al.; licensee Springer. 2015 The Author(s) 2015 |
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| Keywords | corrected three-point quadrature formulae Grüss inequality 26D20 Chebyshev functional corrected Euler Bullen-Simpson formula 26D99 26D15 |
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| References | Dragomir (CR4) 2003; 4 Izumino, Pečarić, Tepeš (CR5) 2005; 2005 Vukelić (CR8) 2009; 3 Dedić, Matić, Pečarić (CR3) 2001; 41 Ujević (CR7) 2000; 250 Ujević, Roberts (CR1) 2004; 45 Mitrinović, Pečarić, Fink (CR2) 1993 Abramowitz, Stegun (CR13) 1965 Franjić, Pečarić, Perić (CR10) 2007; 45 Cerone, Dragomir (CR9) 2014; 8 Matić, Pečarić, Vukelić (CR15) 2005; 35 Franjić, Pečarić (CR16) 2006; 21 Bullen (CR14) 1978; 602-633 Franjić, Pečarić, Perić, Vukelić (CR12) 2011 Pachpatte (CR6) 2006; 7 Aglić Aljinović, Čivljak, Kovač, Pečarić, Ribičić Penava (CR11) 2013 I Franjić (603_CR10) 2007; 45 N Ujević (603_CR1) 2004; 45 BG Pachpatte (603_CR6) 2006 603_CR4 S Izumino (603_CR5) 2005; 2005 P Cerone (603_CR9) 2014; 8 I Franjić (603_CR12) 2011 A Vukelić (603_CR8) 2009; 3 PS Bullen (603_CR14) 1978; 602-633 N Ujević (603_CR7) 2000; 250 M Matić (603_CR15) 2005; 35 DS Mitrinović (603_CR2) 1993 603_CR13 I Franjić (603_CR16) 2006; 21 L Dedić (603_CR3) 2001; 41 A Aglić Aljinović (603_CR11) 2013 |
| References_xml | – volume: 4 issue: 2 year: 2003 ident: CR4 article-title: Some Grüss-type inequalities in inner product spaces publication-title: J. Inequal. Pure Appl. Math. – volume: 21 start-page: 105 year: 2006 end-page: 123 ident: CR16 article-title: On corrected Bullen-Simpson’s inequality publication-title: Bull. Allahabad Math. Soc. – year: 2011 ident: CR12 publication-title: Euler Integral Identity, Quadrature Formulae and Error Estimations – year: 1965 ident: CR13 publication-title: Handbook of Mathematical Functions: With Formulae, Graphs and Mathematical Tables – volume: 8 start-page: 159 issue: 1 year: 2014 end-page: 170 ident: CR9 article-title: Some new Ostrowski-type bounds for the Čebyšev functional and applications publication-title: J. Math. Inequal. doi: 10.7153/jmi-08-10 – volume: 3 start-page: 559 issue: 4 year: 2009 end-page: 566 ident: CR8 article-title: Estimations of the error for general Simpson type formulae via pre-Grüss inequality publication-title: J. Math. Inequal. doi: 10.7153/jmi-03-54 – volume: 2005 start-page: 277 issue: 3 year: 2005 end-page: 288 ident: CR5 article-title: A Grüss-type inequality and its applications publication-title: J. Inequal. Appl. doi: 10.1155/JIA.2005.277 – volume: 250 start-page: 494 year: 2000 end-page: 511 ident: CR7 article-title: A new generalization of Grüss inequality in inner product spaces publication-title: J. Math. Anal. Appl. doi: 10.1006/jmaa.2000.6977 – year: 1993 ident: CR2 publication-title: Classical and New Inequalities in Analysis doi: 10.1007/978-94-017-1043-5 – year: 2013 ident: CR11 publication-title: General Integral Identities and Related Inequalities – volume: 602-633 start-page: 97 year: 1978 end-page: 103 ident: CR14 article-title: Error estimates for some elementary quadrature rules publication-title: Publ. Elektroteh. Fak. Univ. Beogr., Ser. Mat. Fiz. – volume: 41 start-page: 843 year: 2001 end-page: 856 ident: CR3 article-title: Some inequalities of Euler-Grüss type publication-title: Comput. Math. Appl. doi: 10.1016/S0898-1221(00)00324-2 – volume: 35 start-page: 1727 year: 2005 end-page: 1754 ident: CR15 article-title: On generalization of Bullen-Simpson’s inequality publication-title: Rocky Mt. J. Math. doi: 10.1216/rmjm/1181069660 – volume: 45 start-page: 355 issue: 3-4 year: 2007 end-page: 370 ident: CR10 article-title: Quadrature formulae of Gauss type based on Euler identities publication-title: Math. Comput. Model. doi: 10.1016/j.mcm.2006.05.009 – volume: 45 start-page: 41 issue: E year: 2004 end-page: 56 ident: CR1 article-title: A corrected quadrature formula and applications publication-title: ANZIAM J. – volume: 7 issue: 1 year: 2006 ident: CR6 article-title: On Čebyšev-Grüss type inequalities via Pečaric’s extension of the Montgomery identity publication-title: J. Inequal. Pure Appl. Math. – ident: 603_CR4 – volume-title: General Integral Identities and Related Inequalities year: 2013 ident: 603_CR11 – volume: 2005 start-page: 277 issue: 3 year: 2005 ident: 603_CR5 publication-title: J. Inequal. Appl doi: 10.1155/JIA.2005.277 – volume: 3 start-page: 559 issue: 4 year: 2009 ident: 603_CR8 publication-title: J. Math. Inequal doi: 10.7153/jmi-03-54 – volume: 45 start-page: 355 issue: 3-4 year: 2007 ident: 603_CR10 publication-title: Math. Comput. Model doi: 10.1016/j.mcm.2006.05.009 – volume: 41 start-page: 843 year: 2001 ident: 603_CR3 publication-title: Comput. Math. Appl doi: 10.1016/S0898-1221(00)00324-2 – volume-title: J. Inequal. Pure Appl. Math year: 2006 ident: 603_CR6 – volume: 602-633 start-page: 97 year: 1978 ident: 603_CR14 publication-title: Publ. Elektroteh. Fak. Univ. Beogr., Ser. Mat. Fiz – volume: 250 start-page: 494 year: 2000 ident: 603_CR7 publication-title: J. Math. Anal. Appl doi: 10.1006/jmaa.2000.6977 – ident: 603_CR13 – volume: 35 start-page: 1727 year: 2005 ident: 603_CR15 publication-title: Rocky Mt. J. Math doi: 10.1216/rmjm/1181069660 – volume: 45 start-page: 41 issue: E year: 2004 ident: 603_CR1 publication-title: ANZIAM J – volume-title: Classical and New Inequalities in Analysis year: 1993 ident: 603_CR2 doi: 10.1007/978-94-017-1043-5 – volume: 8 start-page: 159 issue: 1 year: 2014 ident: 603_CR9 publication-title: J. Math. Inequal doi: 10.7153/jmi-08-10 – volume-title: Euler Integral Identity, Quadrature Formulae and Error Estimations year: 2011 ident: 603_CR12 – volume: 21 start-page: 105 year: 2006 ident: 603_CR16 publication-title: Bull. Allahabad Math. Soc |
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| Snippet | We obtain some new Grüss type inequalities for the general corrected three-point quadrature formulae of Euler type. As special cases, we derive some new bounds... |
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| Title | Some Grüss type inequalities and corrected three-point quadrature formulae of Euler type |
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