抽象锥中1-集压缩映射的不动点定理  

FIXED POINT THEOREMS FOR 1-SET-CONTRA CTION MAPPINGS IN ABSTRACT CONES

作　　者：张洪谦[1] 刘许成[1] 

机构地区：[1]潍坊学院数学系,山东潍坊261043

出　　处：《常德师范学院学报（自然科学版）》2002年第4期9-10,12,共3页Journal of Changde Teachers University

摘　　要：设P是实Banach空间E的一个锥 ,f是PR 到P的一个 1-集压缩映射 ,且对PR中任一序列 {xn} ,若limn→∞(xn-f(xn) ) =θ,则存在u∈PR,使得u -f(u) =θ.那么当对任意满足‖f(x)‖ >R的x∈ PR,存在y∈IpR(x) ,使‖y-f(x)‖<‖x-f(x)‖ ,或都有‖f(x) -x‖≠‖f(x)‖ -R ,或存在 1<α <+∞ ,使‖f(x)‖α-Rα≤‖f(x) -x‖α,或存在 0<β<1,使‖f(x)‖β-Rβ≥‖f(x) -x‖β,或对任意 0 <λ<1,都有x≠λf(x)时 ,f在PR 中有一个不动点 .通过以上结论的给出 ,解决了一类微积分方程的解的存在性 .Let P be a cone of real Banach space E Suppose that f is a 1-set-contraction map of P R into P ,and {x n} is any sequence in P R such that lim n→∞(x n-f(x n))=θ ,then there exists u∈P R with u-f(u)=θ .Then,that f has a fixed point in P R if some conditions be satisfied.And then this result was applied to the integrodifferential equation,the existence of solutions was obtained also.

关 键 词：抽象锥 1-集压缩映射 不动点定理 k-集压缩映射 非紧性测度 BANACH空间 

分 类 号：O177.91[理学—数学]