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| 研究生： |
曾冠逞 Guan-Cheng Zeng |
|---|---|
| 論文名稱： |
Hardy-Hilbert型式的不等式和Cauchy加法映射的穩定性 On Hardy-Hilbert Type Inequalities and Stability of Cauchy Additive Mappings |
| 指導教授： |
林欽誠
Chin-cheng Lin 蕭勝彥 Sen-Yen Shaw |
| 口試委員: | |
| 學位類別： |
碩士 Master |
| 系所名稱： |
理學院 - 數學系 Department of Mathematics |
| 畢業學年度： | 96 |
| 語文別： | 中文 |
| 論文頁數： | 49 |
| 中文關鍵詞： | 近乎線性映射 、穩定性 、Holder''s 不等式 、Hardy-Hilbert 型式的不等式 、Norm 、積分算子 |
| 外文關鍵詞： | Approximately linear mapping, stability, Holder''s inequality, inequality of Hardy-Hilbert type, integral operator, Norm |
| 相關次數： | 點閱：26 下載：0 |
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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。
This 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.
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[6] C. Park, Y. Cho and M. Han, Functional inequalities associated with Jordan-Von Neumann type additive functional equations, J. Inequal. Appl. (2007), to appear.
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[11] B. Yang, On the norm of a self-adjoint operator and applications to the Hilbert’s type inequalities, Bulletin of the Belgian Mathematical Society, 13 (2006), 577-584.
[12] B. Yang, On the norm of a certain self-adjoint integral operator and applications to bilinear integral inequalities, Taiwanese J. Math., to apprar.
[13] D. H. Zhang and H. X. Cao, Stability of functional equations in several variables, Acta Math. Sinica. (Engl. Ser.) 23 (2007), 321-326.
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