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ON NEW OSTROWSKI TYPE INEQUALITIES

ON NEW OSTROWSKI TYPE INEQUALITIES DEMONSTRATIO MATHEMATICAVol. X L INo 22008Wenjun Liu, Jianwei DongON N E W OSTROWSKI TYPE INEQUALITIESAbstract. In this short note, some new inequalities of Ostrowski type involving twofunctions and their derivatives for mapping whose derivations belong to Lp[a, 6], ρ > 1are established.1. IntroductionIn 1938, Ostrowski proved the following interesting integral inequality[5]:THEOREM 1. Let / : [A, ft] —» M be continuous on [A, ft] and differentiablein (a, ft) and its derivative f : (a, ft) —> R is bounded in (a, ft), that is,ll/'lloo : = sup |/'(ÍC)| < oo. Then for any χ G [a, ft], we have the inequality:te(a,b)(1.1)f(x)ft — a\f(t)dt<1,( χ - Ψ )(ft - a)"2(b-a)\\f'\The inequality is sharp in the sense that the constant 1/4 cannot be replacedby a smaller one.In [1], Dragomir and Wang gave a generalization of Ostrowski integralinequality for mappings whose derivatives belong to LP[a, ft], p> 1.THEOREM 2. Let f : [a,ft]—> R be continuous on [a,ft]and differentiablein (a, ft) and its derivative f: (a, ft) —> R is bounded in (a, ft), that is,This work was supported by the Science Research Foundation of NUIST, theNatural Science Foundation of Jiangsu Province Education Department under GrantNo.07KJD510133 and the Youth Natural Science Foundation http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

ON NEW OSTROWSKI TYPE INEQUALITIES

Demonstratio Mathematica , Volume 41 (2): 6 – Apr 1, 2008

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References (5)

Publisher
de Gruyter
Copyright
© by Wenjun Liu
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-2008-0209
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATIO MATHEMATICAVol. X L INo 22008Wenjun Liu, Jianwei DongON N E W OSTROWSKI TYPE INEQUALITIESAbstract. In this short note, some new inequalities of Ostrowski type involving twofunctions and their derivatives for mapping whose derivations belong to Lp[a, 6], ρ > 1are established.1. IntroductionIn 1938, Ostrowski proved the following interesting integral inequality[5]:THEOREM 1. Let / : [A, ft] —» M be continuous on [A, ft] and differentiablein (a, ft) and its derivative f : (a, ft) —> R is bounded in (a, ft), that is,ll/'lloo : = sup |/'(ÍC)| < oo. Then for any χ G [a, ft], we have the inequality:te(a,b)(1.1)f(x)ft — a\f(t)dt<1,( χ - Ψ )(ft - a)"2(b-a)\\f'\The inequality is sharp in the sense that the constant 1/4 cannot be replacedby a smaller one.In [1], Dragomir and Wang gave a generalization of Ostrowski integralinequality for mappings whose derivatives belong to LP[a, ft], p> 1.THEOREM 2. Let f : [a,ft]—> R be continuous on [a,ft]and differentiablein (a, ft) and its derivative f: (a, ft) —> R is bounded in (a, ft), that is,This work was supported by the Science Research Foundation of NUIST, theNatural Science Foundation of Jiangsu Province Education Department under GrantNo.07KJD510133 and the Youth Natural Science Foundation

Journal

Demonstratio Mathematicade Gruyter

Published: Apr 1, 2008

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