| DC 欄位 |
值 |
語言 |
| DC.contributor | 數學系 | zh_TW |
| DC.creator | 曾冠逞 | zh_TW |
| DC.creator | Guan-Cheng Zeng | en_US |
| dc.date.accessioned | 2008-4-14T07:39:07Z | |
| dc.date.available | 2008-4-14T07:39:07Z | |
| dc.date.issued | 2008 | |
| dc.identifier.uri | http://ir.lib.ncu.edu.tw:88/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.description | National Central University | en_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.abstract | 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. | en_US |
| DC.subject | 近乎線性映射 | zh_TW |
| DC.subject | 穩定性 | zh_TW |
| DC.subject | Holder's 不等式 | zh_TW |
| DC.subject | Hardy-Hilbert 型式的不等式 | zh_TW |
| DC.subject | Norm | zh_TW |
| DC.subject | 積分算子 | zh_TW |
| DC.subject | Approximately linear mapping | en_US |
| DC.subject | stability | en_US |
| DC.subject | Holder's inequality | en_US |
| DC.subject | inequality of Hardy-Hilbert type | en_US |
| DC.subject | integral operator | en_US |
| DC.subject | Norm | en_US |
| DC.title | Hardy-Hilbert型式的不等式和Cauchy加法映射的穩定性 | zh_TW |
| dc.language.iso | zh-TW | zh-TW |
| DC.title | On Hardy-Hilbert Type Inequalities and Stability of Cauchy Additive Mappings | en_US |
| DC.type | 博碩士論文 | zh_TW |
| DC.type | thesis | en_US |
| DC.publisher | National Central University | en_US |