| Banach空间中的幂级数方程 |
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| 引用本文： | 胡适耕,洪世煌.Banach空间中的幂级数方程[J].华中科技大学学报(自然科学版),1992(3). |
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| 作者姓名： | 胡适耕 洪世煌 |
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| 作者单位： | 华中理工大学数学系
(胡适耕)，华中理工大学数学系(洪世煌) |
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| 摘 要： | 本文考虑Banach空间中形如x=u+sum from k=1 to ∞(a_kx~k)的幂级数方程,建立了一个比较定理,并将其应用于一定的非线性积分方程.
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| 关 键 词： | 幂级数方程 压缩映射 积分方程 |
A Power Series Equation in Banach Space |
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| Hu Shigeng Hong Shihuang.A Power Series Equation in Banach Space[J].JOURNAL OF HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY.NATURE SCIENCE,1992(3). |
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| Authors: | Hu Shigeng Hong Shihuang |
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| Institution: | Hu Shigeng Hong Shihuang |
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| Abstract: | A power series equation in Banach space of the form x=u+ isconsidered. By means of the principle of contraction mapping, a comparison theorem is developed which describes the relation between the equationx =u+ another power series equation x= u +. Some re-suits concerning the solutions for the first equation are obtained from certain information about the solutions for the second equation that isprobably simpler than the initial equation. The results have been appliedto the so-called Hammerstein integral equation of the form x(t) = G(t,s)f(s,x(s))ds. Specific examples are considered and certain numerical results are obtained. |
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| Keywords: | power series equation contraction mapping integral equation |
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