p-线性空间的不动点定理和非线性选择原理的建立  

Fixed Point Theorems and Principles of Nonlinear Alternatives in p-vector Spaces

作　　者：袁先智 George Xian Zhi YUAN(College of Science,Chongqing University of Technology,Chongqing 400054,P.R.China;Business School,Chengdu University,Chengdu 610106,P.R.China;School of Mathematics,Sichuan University,Chengdu 610065,P.R.China;School of Business,Sun Yat-Sen University,Guangzhou 510275,P.R.China;School of Business,East China University of Science and Technology,Shanghai 200237,P.R.China)

机构地区：[1]重庆理工大学理学院,重庆400054 [2]成都大学商学院,成都610106 [3]四川大学数学学院,成都610065 [4]中山大学管理学院,广州51027 [5]华东理工大学商学院,上海200237

出　　处：《数学学报（中文版）》2024年第5期962-986,共25页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(71971031,U1811462)。

摘　　要：本文的目标是在一般的p-线性空间和局部p-凸空间框架下建立针对单值和拟上半连续集值映射的不动点定理、最佳逼近定理、和对应的Leray-Schauder非线性(二择一)选择原理,这里p∈(0,1].我们建立的不动点定理是在p-线性空间和局部p-凸空间对Schauder猜想的肯定答复,对应的最佳逼近定理和Leray-Schauder选择原理也是非线性泛函分析的核心工具.这些新结果统一和推广了目前在数学文献中存在的理论成果,也是对作者最近工作([Fixed Point Theory Algorithms Sci.Eng.,2022,2022:Paper Nos.20,26])的继续和深度发展.The goal of this paper is to develop new fixed points,best approximation,and Leray-Schauder alternative for single-valued and(quasi) upper semicontinuous(QUSC) set-valued mapping in p-vector spaces and locally p-convex spaces,where p∈(0,1]The fixed point theorem established in this paper is a positive answer to Schauder conjecture in p-vector spaces and locally p-convex spaces;the corresponding best approximation theorem and the principle of Leray-Schauder alternative are also the fundamental tools in nonlinear functional analysis under the framework of p-vector spaces and locally p-convex spaces.These new results unify and generalize the theoretical results existing in the current mathematical literature,and they are also the continuation and in-depth development of the recent work did by Yuan [Fixed Point Theory Algorithms Sci.Eng.,2022,2022:Paper Nos.20,26],and related references.

关 键 词：非线性分析 p-线性空间 局部p-凸空间(0Schauder猜想 SCHAUDER不动点定理 图逼近 最佳逼近 Rothe型不动点 Leray-Schauder二择一原理 拟上半连续(QUSC) 

分 类 号：O177.91[理学—数学]