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    Title: 離散型Opial不等式的研究
    Other Titles: On Discrete Opial's Inequality
    Authors: 楊國勝
    Contributors: 淡江大學數學學系
    Keywords: 非遞減;離散型Opial不等式
    Date: 2006
    Issue Date: 2009-03-16 12:51:11 (UTC+8)
    Abstract: Lee [5] 於1968年証明如下的離散型Opial不等式:設{}∞=1iiu為非遞減且非負的數列,00=u, 若p > 0,q > 0,或p < 0,q < 0,則 1?+qp (2) ΣΣ=+?=????niqpiinnipiqiiuuKuuu1111)()( 其中)(0qpqK+=,而K,3,2,1=n時 ??????++++=??)()1(,)(max11qpnqqppnKKppnn。 若p > 0,q < 0,,或p < 0,q > 0,1?+qp0≠+qp1?+qp,則 (3) ΣΣ=+?=????niqpiinnipiqiiuuCuuu1111)()( 其中)(0qpq+=C,而K,3,2,1=n時 ??????++++=??)()1(,)(min11qpnqqppnCCppnn 在(i) p > 0,q > 0,,或 (ii) p > 0,q < 0,1?+qp1?+qp或 (iii) p > 0,q < 0,1?+qp,不等式(2)或(3),是否成立,是一個尚未解決的問題,本計劃的目的就是在研究這個問題。
    Appears in Collections:[數學學系暨研究所] 研究報告

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