半范空间上一类非线性算子的近似判据  

Approximate Criteria for a Class of Nonlinear Operators on Semi-Norm Spaces

作　　者：邢志勇[1] 蔡俊娟[1] 黄丽[2] XING Zhiyong;CAI Junjuan;HUANG Li(Xaimen Ocean Vocational College,Xiamen 361100,Fujian,China;Taiyuan University of Science and Technology,Taiyuan 030024,Shanxi,China)

机构地区：[1]厦门海洋职业技术学院公共教育学院,福建厦门361100 [2]太原科技大学应用科学学院,山西太原030024

出　　处：《山西师范大学学报（自然科学版）》2023年第1期14-16,共3页Journal of Shanxi Normal University(Natural Science Edition)

基　　金：厦门海洋职业技术学院高层次人才科研专项立项项目(KYG202001)。

摘　　要：非线性算子又称非线性映射,非线性映射是一种对比较复杂的数据结构进行直观分类和识别的多元统计分析方法.泛函分析的研究对象主要是线性算子及其特殊情况线性泛函,但是,自然界和工程技术中出现的大量问题都是非线性的.数学物理中的一些线性方程其实都是在一定条件下的近似.以一类连续的非线性算映射作为研究对象,通过对半范空间上的连续非线性映射的渐进分析,给出此类非线性映射的近似判据,提出通过添加代数性质的方法,给出了非线性映射问题在特定条件下的近似判据.但是研究仅仅是针对一类非线性映射问题,不具有普遍性.由于非线性映射在于非线性方程之中,从而有关非线性映射的理论就围绕着非线性方程的求解的研究而展开.考察非线性映射的特征,解释非线性现象,需要对大量的非线性映射进行研究,才能从中提炼具有普适的非线性映射理论.Nonlinear operators are also called nonlinear mapping,which is a multivariate statistical analysis method for intuitive classification and identification of complex data structures.The research object of functional analysis is linear operator and its special case linear functional.But a lot of problems in nature and engineering are nonlinear.Some linear equations in mathematical physics are approximations under certain conditions.In this paper,we take a class of continuous nonlinear mapping as the research object,and give the approximate criterion of this kind of nonlinear mapping through the asymptotic analysis of continuous nonlinear mapping on semi-normal space.In this paper,the approximate criterion of nonlinear mapping problem under certain conditions is given by adding algebraic properties.However,the research in this paper is only for a class of nonlinear mapping problems,which is not universal.Since the nonlinear mapping lies in the nonlinear equation,the theory of nonlinear mapping revolves around the study of the solution of the nonlinear equation.To investigate the characteristics of nonlinear mappings and explain nonlinear phenomena,it is necessary to study a large number of nonlinear mappings so as to extract the universal theory of nonlinear mappings.

关 键 词：非线性算子 解剖算子 吸收算子 

分 类 号：O177[理学—数学]