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 The Banach Space Characteristic Inequality Equation Quantity Law and its Application |
Author:Xu Zongben Jiang Yaoling Xu Honggun
School:Xian Jiaotong University,School of Science
The results of this project fall into the field of the functional analysis of the mathematics discipline and applied mathematics. The characteristic inequality quantity law corresponding to the Hibert space ¡°parallelogram law¡± and ¡°binominal equation¡± is established concentrated in the Banach space and applied to vast problems of the applied mathematics. Its main contents include the following:
1. The characteristic inequality quantity law in the Lp space is discovered and proved.
2. The Pth characteristic inequality quantity law mutually supplementary with Lp second characteristic inequality quantity law is established.
3. The characteristic inequality quantity law of the uniformly convex and uniformly smooth Banach space is established.
4. The sufficient and necessary conditions of the strong and weak convergence of the non-linear compression half-group are completely delineated.
5. A series of the above characteristic inequality quantity laws are applied to vast fields such as the fixed point theory, argotic theory, approximation theory, non-linear functional analysis, numeric analysis, etc. and a group of deepgoing results keeping a leading position both at home and abroad are acquired.
The results of this project feature specifically: 1) the ¡°fundamentality¡± of the object under research and 2) the ¡°extensiveness¡± of the applicability of the research results. In addition, all the conclusions are arrived at on the sufficient and necessary conditions. So the results also feature 3) the ¡°originality¡± of the results and 4) the ¡°completeness¡± of the conclusions.
Application and popularization: With the project, there are altogether 21 papers published. From them, 12 papers were collected by SCI and cited for 167 times by 104 papers (in which are included the 139 citations by other 89 papers). Among the 89 papers with the citations by others, there are 49 papers applying the results of this paper in a substantial way (used as the introductory or preparatory theorem). The application fields are involved with approximation theory, functional analysis, fixed-point theory and artificial intelligence, etc. The authors making the citation are associated with those in more than 10 countries like Poland, Germany, US, Japan, South Korean, Italy, UK, Spain, China, etc. 35 from the 89 papers are related to the popularization and improvement of the results of this project. Among the project papers cited, the highest citation rate for a single paper is 59 times, with the SCI high citation rate award of the international ISI given in 2000.
The results of the project have provided a deepgoing ¡°quantization¡± tool for researching on various kinds of problems in the Banach space. As a result, a series of the solutions of problems of applied and computational mathematics are related to the application of the research of quantitative nature. Specifically, the inequality characteristic quantity law of the Banach space developed by the results of the project has become one of the basic tools to research on the discrete approximation of the dissipation system in the non-linear functional analysis field.
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Copyright
2001-2004
by
Science and Technology Office of
Xi'an Jiaotong University. All rights reserved.
Last modified time:
2010-9-9 17:00 |
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