與廣義海倫平均有關(guān)的冪平均精確界.pdf

1、河北大學(xué)碩士學(xué)位論文與廣義海倫平均有關(guān)的冪平均精確界姓名：于萬國申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：高紅亞2011-05AbstractAbstractVarious means and their sharp estimates have many applications in physics, me-chanics and engineering. In particular, many remarkable inequal

2、ities for Heronian andgeneralized Heronian means have been found by many mathematicians. In this paper, wecontinue to study the inequalities on generalized Heronian means. We find the optimalvalues for α, β, γ and τ, suc

3、h that the inequalitiesHα(a, b) 0 with a ?= b. Here, Hω(a, b), Ar(a, b), P(a, b) and L(a, b) be thegeneralized Heronian, power, Seiffert and logarithmic means of two positive numbers aand b, respectively.Keywords Sharp