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S. Dragomir, Song Wang (1998)
Applications of Ostrowski's inequality to the estimation of error bounds for some special means and for some numerical quadrature rules☆Applied Mathematics Letters, 11
(2006)
NOTE ON QI'S INEQUALITY AND BOUGOFFA'S INEQUALITYJournal of Inequalities in Pure & Applied Mathematics, 7
S. Dragomir, P. Cerone, J. Roumeliotis (2000)
A new generalization of Ostrowski's integral inequality for mappings whose derivatives are bounded and applications in numerical integration and for special meansAppl. Math. Lett., 13
S. Dragomir, Sean Wang (1998)
A new inequality of Ostrowski''s type in Lp-norm
B. Pachpatte (2002)
A NOTE ON OSTROWSKI TYPE INEQUALITIESDemonstratio Mathematica, 35
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
Demonstratio Mathematica – de Gruyter
Published: Apr 1, 2008
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