两个严格的加权Ostrowski型不等式
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摘要
使用Cauchy积分不等式和Grüss不等式的变式得到两个严格的加权Ostrowski型不等式.
Two sharp weighted Ostrowski type integral inequalities are established by using Cauchy integral inequality and the variant of Grüss′inequality.
Two sharp weighted Ostrowski type integral inequalities are established by using Cauchy integral inequality and the variant of Grüss′inequality.
引文
[1]Dragomir S S,Agarwal R P,Cerone P.On Simpson′s inequality and applications[J].J.of Inequal.Appl.,2000,5(6):533-579.
[2]Ostrowski A.ber die Absolutabweichung einer differentiierbaren Funktion von ihrem Integralmittelwert[J].Comment.Math.Helv.,1938,10(1):226-227.
[3]Ujevi'c N.Sharp inequalities of Simpson type and Ostrowski type[J].Comput.Math.Appl.,2004,48(1):145-151.
[4]Liu Z.Note on a paper by N.Ujevi'c[J].Applied Mathematics Letters,2007,20(6):659-663.
[5]Shi Y X,Liu Z.Some sharp Simpson type inequalities and applications[J].Applied Mathematics E-Notes,2009,9(7):205-215.
[6]Tseng K L,Yang G S,Dragomir S S.On weighted Simpson type inequalities and applications[J].J.Math Inequal.,2007,1(1):13-22.
[7]Peˇcari'c J,Tseng K L.New weighted Simpson type inequalities and their applications[J].J.Math Inequal.,2007,1(3):321-337.
[8]Tseng K L,Hwang S R,Dragomir S S.Generalizations of weighted Ostrowski type inequalities for mapping of bounded variation and their applications[J].Computers and Mathematics with Applications,2008,55(8):1785-1793.
[9]Tseng K L,Hwang S R,Yang G S,etal.Weighted Ostrowski integral inequality for mappings of bounded variation[J].Taiwanese Journal of Mathematics,2011,15(2):573-585.
[10]Alomari M W.A companion of Dragomir′s generalization of Ostrowski′s inequality and applications in numerical integration[J].RGMIA Res.Rep.Coll.,2011(14),Article 50.
[11]Cheng X L,Sun J.A note on the perturbed trapezoid inequality[J].J.Inequal.Pure Appl.Math.,2002,3(2),Article 29.
[2]Ostrowski A.ber die Absolutabweichung einer differentiierbaren Funktion von ihrem Integralmittelwert[J].Comment.Math.Helv.,1938,10(1):226-227.
[3]Ujevi'c N.Sharp inequalities of Simpson type and Ostrowski type[J].Comput.Math.Appl.,2004,48(1):145-151.
[4]Liu Z.Note on a paper by N.Ujevi'c[J].Applied Mathematics Letters,2007,20(6):659-663.
[5]Shi Y X,Liu Z.Some sharp Simpson type inequalities and applications[J].Applied Mathematics E-Notes,2009,9(7):205-215.
[6]Tseng K L,Yang G S,Dragomir S S.On weighted Simpson type inequalities and applications[J].J.Math Inequal.,2007,1(1):13-22.
[7]Peˇcari'c J,Tseng K L.New weighted Simpson type inequalities and their applications[J].J.Math Inequal.,2007,1(3):321-337.
[8]Tseng K L,Hwang S R,Dragomir S S.Generalizations of weighted Ostrowski type inequalities for mapping of bounded variation and their applications[J].Computers and Mathematics with Applications,2008,55(8):1785-1793.
[9]Tseng K L,Hwang S R,Yang G S,etal.Weighted Ostrowski integral inequality for mappings of bounded variation[J].Taiwanese Journal of Mathematics,2011,15(2):573-585.
[10]Alomari M W.A companion of Dragomir′s generalization of Ostrowski′s inequality and applications in numerical integration[J].RGMIA Res.Rep.Coll.,2011(14),Article 50.
[11]Cheng X L,Sun J.A note on the perturbed trapezoid inequality[J].J.Inequal.Pure Appl.Math.,2002,3(2),Article 29.