凸函數(shù)在證明不等式中的應(yīng)用(已修改)
2025-07-05 16:21 本頁(yè)面
【正文】 摘要凸性是一種重要的幾何性質(zhì)，凸函數(shù)在泛函分析，最優(yōu)化理論，同時(shí)討論了凸函數(shù)的幾條常用性質(zhì)，最后重點(diǎn)展示了凸函數(shù)在證明不等式中的應(yīng)用.關(guān)鍵詞: 凸函數(shù)，凸性，判定定理，不等式 AbstractConvexity is an important geometric property. Convex function have extensive applications in functional analysis, optimal theory and mathematical economy. This article first has given the definition of convex function and its decision theorem, meanwhile discussed convex function several monly used nature，lastly has demonstrated the convex function in inequality proof application.Keywords：convex function，convexity, decision theorem, Jensen inequality 凸函數(shù)在證明不等式中的應(yīng)用1 引言在數(shù)學(xué)思想方法中，函數(shù)思想是一種很重要的思想方法，其精髓在于利用函數(shù)的相關(guān)性質(zhì)對(duì)討論的問(wèn)題進(jìn)行推理和論證，進(jìn)而尋求解決問(wèn)題的途徑.凸函數(shù)是一類重要的函數(shù)，現(xiàn)已成為數(shù)學(xué)規(guī)劃、對(duì)策論、數(shù)理經(jīng)濟(jì)學(xué)、凸函數(shù)作為一類特殊函數(shù)，在現(xiàn)代優(yōu)化學(xué)、運(yùn)籌學(xué)、, 對(duì)風(fēng)險(xiǎn)厭惡的度量, 也可以表現(xiàn)為對(duì)效用函數(shù)凸性的選擇，函數(shù)的凸性是函數(shù)在區(qū)間上變化的整體性態(tài)，把握函數(shù)在區(qū)間上的整體性態(tài)，不僅可以更加科學(xué)、準(zhǔn)確地描繪出函數(shù)的圖象，而且有助于對(duì)函數(shù)的定
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