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  • 學位論文

集值級數的根式審斂法

The Root Test for Series of Sets

指導教授 : 李金城

摘要


集值函數分析(set valued analysis)近幾年引起相當程度注意。本篇論文主要是討論賦範線性空間(normed linear space)中集值級數的一些歛散性質,藉由賦距空間(metric space)中集值序列的庫氏收斂( Kuratowski convergence)概念,我們推廣了傳統高等微積分中的根式審歛法 (root test)。

並列摘要


The set valued analysis has caused much more attention in recent years. This paper is mainly talking about the convergence and divergence for series of sets in normed linear space with the concept of Kuratowski convergence in metric space. Then, we generalize the root test in advance calculus to the case of set-valued series.

並列關鍵字

Series of Sets The Root Test

參考文獻


[2] Aubin ,J.P.(1977).Applied Abstract Analysis, John Wiley and Sons Inc.
[6] 袁重雄 (2010) Absolutely convergent Series of Sets,中原大學 , 碩士論文
[1] Aubin ,J.P. and H.Frankowska (1990).Set-valued Analysis, ,Boston.
[3] K. Kuratowski(1966) Topologic, Vols.1 and 2.Academic Press.
[4] H.C. Lai and J.C.Lee(1997) Upper Limit of Sets and Continuous Mapping. Far East J. Math. Sci. 5(4),505-514.

被引用紀錄


黃惠玲(2012)。歐氏空間之集合級數豪斯多夫距離下之柯西並 項審斂法〔碩士論文,中原大學〕。華藝線上圖書館。https://doi.org/10.6840/cycu201200166

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