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Open AccessArticle10.1515/dema-2013-0295

On a refinement of the majorisation type inequality

Muhammad Adil Khan,Marek Niezgoda,‎Josip Pečarić-2011-03-01-Demonstratio Mathematica
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Abstract In this note, two mean value theorems are proved by using some recent results by Barnett et al. [N. S. Barnett, P. Cerone, S. S. Dragomir, Majorisation inequalities for Stieltjes integrals , Appl. Math. Lett. 22 (2009), 416-421]. A new class of Cauchy type means for two functions is studied. Logarithmic convexity for differences of power means is proved. Monotonicity of Cauchy means is shown.

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Abstract In this note, two mean value theorems are proved by using some recent results by Barnett et al. [N. S. Barnett, P. Cerone, S. S. Dragomir, Majorisation inequalities for Stieltjes integrals , Appl. Math. Lett. 22 (2009), 416-421]. A new class of Cauchy type means for two functions is studied. Logarithmic convexity for differences of power means is proved. Monotonicity of Cauchy means is shown.

Keywords

MathematicsInequalityType (biology)Calculus (dental)Algebra over a fieldPure mathematicsMathematical economicsMathematical analysis

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