博碩士論文 942201008 完整後設資料紀錄

DC 欄位 語言
DC.contributor數學系zh_TW
DC.creator曾冠逞zh_TW
DC.creatorGuan-Cheng Zengen_US
dc.date.accessioned2008-4-14T07:39:07Z
dc.date.available2008-4-14T07:39:07Z
dc.date.issued2008
dc.identifier.urihttp://ir.lib.ncu.edu.tw:444/thesis/view_etd.asp?URN=942201008
dc.contributor.department數學系zh_TW
DC.description國立中央大學zh_TW
DC.descriptionNational Central Universityen_US
dc.description.abstract這篇論文研究兩個主題:Hardy-Hilbert型式的積分不等式和Cauchy加法映射的穩定性。 下列是主要結果:1) 將B. Yang對某種有界的自伴積分算子T : L2 (0,∞) → L2 (0,∞) 的範數及其應用到Hardy -Hilbert型式的不等式的結果, 從 L2 (0,∞)空間推廣到Lp (0,∞) 空間 (p > 1) ; 2) 推廣Rassias關於Cauchy加法映射的穩定性定理; 3) 給予Park等人[6]的定理的一個正確的證明; 4) 以一個唯一的群的同態變換 (或環的同態變換) 去逼近一個特定的向量映射的奇部分。zh_TW
dc.description.abstractThis thesis is concerned with two subjects of research; Hardy-Hilbert type inequalities and the stability of Cauchy additive mappings. The following are done : 1) to extend B. Yang’’s result on the norm of a bounded self- adjoint integral operator T : L2 (0,∞) → L2 (0,∞) and its applications to Hardy-Hilbert type integral inequalities from the space L2 (0,∞) to the space Lp (0,∞) with p > 1 ; 2) to generalize Rassias’’s theorem on the stability of Cauchy additive mappings ; 3) to give a correct proof of Park et al’’s theorem in [6]; 4) to approximate the odd part of a certain vector mapping by a unique group homomorphism and ring homomorphism, respectively.en_US
DC.subject近乎線性映射zh_TW
DC.subject穩定性zh_TW
DC.subjectHolder's 不等式zh_TW
DC.subjectHardy-Hilbert 型式的不等式zh_TW
DC.subjectNormzh_TW
DC.subject積分算子zh_TW
DC.subjectApproximately linear mappingen_US
DC.subjectstabilityen_US
DC.subjectHolder's inequalityen_US
DC.subjectinequality of Hardy-Hilbert typeen_US
DC.subjectintegral operatoren_US
DC.subjectNormen_US
DC.titleHardy-Hilbert型式的不等式和Cauchy加法映射的穩定性zh_TW
dc.language.isozh-TWzh-TW
DC.titleOn Hardy-Hilbert Type Inequalities and Stability of Cauchy Additive Mappingsen_US
DC.type博碩士論文zh_TW
DC.typethesisen_US
DC.publisherNational Central Universityen_US

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