【摘要】：本文以星體的對偶Orlicz Hausdorff度量的刻畫問題和星體的對偶混合亮度積分及其極值問題為主要研究對象。我們引進了星體的對偶Orlicz Hausdorff度量的概念,并將其與經(jīng)典的對偶Hausdorff度量和對偶1Hausdorff度量進行了比較。進而討論了這一新度量的一些基本性質(zhì)。這一度量為計算Orlicz空間中星體之間的距離提供了便利。我們還對星體引進了對偶混合亮度積分的概念,進而研究了其相關(guān)極值問題,建立了對不同指數(shù)的循環(huán)不等式,以及它與星體的截面體體積之間的重要聯(lián)系。
[Abstract]:In this paper, we focus on the characterization of dual Orlicz Hausdorff metric of stars and the dual mixed luminance integral and its extremum of stars. We introduce the concept of dual Orlicz Hausdorff metric of stars and compare it with the classical dual Hausdorff metric and dual 1Hausdorff metric. Then some basic properties of this new metric are discussed. This metric facilitates the calculation of distances between stars in Orlicz space. We also introduce the concept of dual mixed luminance integral to the star, and then study its correlation extremum problem, establish the cyclic inequality for different exponents and the important relation between it and the volume of the cross section body of the star.
【學位授予單位】：重慶師范大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O186.5

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相關(guān)期刊論文 前2條

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2 何日高;;p-Hausdorff度量[J];應(yīng)用數(shù)學與計算數(shù)學學報;2011年01期

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本文編號：2241920