论文标题
p矢量空间中的非线性分析，用于单件价值1集的合同映射
Nonlinear Analysis in p-Vector Spaces for Singe-Valued 1-Set Contractive Mappings
论文作者
论文摘要
本文的目的是在p矢量空间的框架下为单个值映射开发一些基本且重要的非线性分析，特别是在（0，1]中，局部p-convex空间。更确切地说，更确切地说，基于单个值的固定点固定位置的固定点为单位p-con的固定点，以建立了一个固定点的固定点，以建立近似p-con的最佳映射。连续冷凝映射随后用于为包括1）缩合的三类非线性映射开发新结果； 2）1集承包商； 3）在局部p-convex空间中的半固定1集合同映射。接下来，它们用于建立非线性替代的一般原理，leray- schauder替代点，非自动映射的固定点，具有不同边界条件的非线性映射的固定点，用于从局部p-convex空间的非线性映射，到局部的无用映射，在均匀的convex banach空间中或具有opial条件的均匀的convex banach空间。本文给出的结果不仅包括现有文献中的相应案例作为特殊案例，而且还预计将是在非线性功能分析中开发新理论的有用工具，并应用于研究P-Vector Space在P-vector Space的一般框架下对P中的实践引起的相关非线性问题的应用（0，1，1，1）。 Finally, the work presented by this paper focuses on the development of nonlinear analysis for single-valued (instead of set-valued) mappings for locally p-convex spaces, essentially, is indeed the continuation of the associated work given recently by Yuan [134] therein, the attention is given to the study of nonlinear analysis for set-valued mappings in locally p-convex spaces for p in (0, 1].
The goal of this paper is to develop some fundamental and important nonlinear analysis for single-valued mappings under the framework of p-vector spaces, in particular, for locally p-convex spaces for p in (0, 1]. More precisely, based on the fixed point theorem of single-valued continuous condensing mapping in locally p-convex spaces as the starting point, we first establish best approximation results for (single-valued) continuous condensing mappings which are then used to develop new results for three classes of nonlinear mappings consisting of 1) condensing; 2) 1-set contractive; and 3) semiclosed 1-set contractive mappings in locally p-convex spaces. Next they are used to establish general principle for nonlinear alternative, Leray - Schauder alternative, fixed points for non-self mappings with different boundary conditions for nonlinear mappings from locally p-convex spaces, to nonexpansive mappings in uniformly convex Banach spaces, or locally convex spaces with Opial condition. The results given by this paper not only include the corresponding ones in the existing literature as special cases, but also expected to be useful tools for the development of new theory in nonlinear functional analysis and applications to the study of related nonlinear problems arising from practice under the general framework of p-vector spaces for p in (0, 1]. Finally, the work presented by this paper focuses on the development of nonlinear analysis for single-valued (instead of set-valued) mappings for locally p-convex spaces, essentially, is indeed the continuation of the associated work given recently by Yuan [134] therein, the attention is given to the study of nonlinear analysis for set-valued mappings in locally p-convex spaces for p in (0, 1].
