四川师范大学学报（自然科学版）
四川師範大學學報（自然科學版）
사천사범대학학보（자연과학판）
JOURNAL OF SICHUAN NORMAL UNIVERSITY(NATURAL SCIENCE)
2010年
2期
156-158
,共3页
变分不等式%例外簇%不动点%零调集值映射
變分不等式%例外簇%不動點%零調集值映射
변분불등식%예외족%불동점%령조집치영사
variational inequality%exceptional family%fixed-point%acyclic set-valued mapping
为研究Banach空间中的集值变分不等式问题,提出了一个新的例外簇概念,并利用零调集值映射的一个Leray-Schauder型不动点定理,证明了变分不等式或有解,或集值映射[J(x)-F(x)]:K→2~(B*)有一例外簇,同时给出了集值映射[J(x)-F(x)]无例外簇的条件.
為研究Banach空間中的集值變分不等式問題,提齣瞭一箇新的例外簇概唸,併利用零調集值映射的一箇Leray-Schauder型不動點定理,證明瞭變分不等式或有解,或集值映射[J(x)-F(x)]:K→2~(B*)有一例外簇,同時給齣瞭集值映射[J(x)-F(x)]無例外簇的條件.
위연구Banach공간중적집치변분불등식문제,제출료일개신적예외족개념,병이용령조집치영사적일개Leray-Schauder형불동점정리,증명료변분불등식혹유해,혹집치영사[J(x)-F(x)]:K→2~(B*)유일예외족,동시급출료집치영사[J(x)-F(x)]무예외족적조건.
In order to study the existence problem of solution to variational inequalities in Banach space,a new exceptional family is introduced.It is proved by using Leray-Schaude type fixed-point theorem of acyclic set-valued mapping that the variational inequality has at least one solution,or the mapping of [J(x)-F(x)]:K→2~(B*) has an exceptional family.The conditions of this set-valued variational inequality without exceptional family are given.
