The best approximation theorems and variational inequalities for discontinuous mappings in Banach spaces  

作　　者：LIU LiShan KONG DeZhou WU YongHong 

机构地区：[1]School of Mathematical Sciences, Qufu Normal University [2]Department of Mathematics and Statistics, Curtin University of Technology [3]College of Information Science and Engineering, Shandong Agricultural University

出　　处：《Science China Mathematics》2015年第12期2581-2592,共12页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11371221);the Specialized Research Foundation for the Doctoral Program of Higher Education of China(Grant No.20123705110001);the Program for Scientific Research Innovation Team in Colleges and Universities of Shandong Province

摘　　要：We discuss Ky Fan's theorem and the variational inequality problem for discontinuous mappings f in a Banach space X. The main tools of analysis are the variational characterizations of the metric projection operator and the order-theoretic fixed point theory. Moreover, we derive some properties of the metric projection operator in Banach spaces. As applications of our best approximation theorems, three fixed point theorems for non-self maps are established and proved under some conditions. Our results are generalizations and improvements of various recent results obtained by many authors.We discuss Ky Fan’s theorem and the variational inequality problem for discontinuous mappings f in a Banach space X. The main tools of analysis are the variational characterizations of the metric projection operator and the order-theoretic fixed point theory. Moreover, we derive some properties of the metric projection operator in Banach spaces. As applications of our best approximation theorems, three fixed point theorems for non-self maps are established and proved under some conditions. Our results are generalizations and improvements of various recent results obtained by many authors.

关 键 词：best approximation theorem variational inequality discontinuous map Ky Fan’s theorem fixed point Banach spaces 

分 类 号：O177.2[理学—数学]