两对相容映射的公共不动点定理  

Common fixed points for two pairs of compatible mappings

作　　者：陈仕洲[1] 

机构地区：[1]韩山师范学院数学系,广东潮州521041

出　　处：《宝鸡文理学院学报（自然科学版）》2004年第1期10-11,18,共3页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

摘　　要：研究了两对相容映射的公共不动点的存在性和唯一性,获得一个新的公共不动点定理:设(f,A)和(g,B)都是X上相容自映射,且(f,A)或(B,g)连续,fX BX,gX AX。如果存在X×X上的非负对称实函数Φ,满足:1)Φ(x,x)=0, x∈X,对每一个变量的任一固定值,Φ(.,.)对另一变量是连续的;2) x,y∈X,Φ(fx,gy)≤βΦ(Ax,By),0≤β<1;3) x,y∈X,有d(fx,gy)≤αmax{d(Ax,By),d(Ax,fx),d(By,gy),12[d(Ax,gy)+d(By,fx)]}+Φ(Ax,By)其中0≤α<1,则f,g,A,B在X中存在唯一公共不动点。The existence and uniqueness of common fixed points for two pairs of compatible mappings are considered,a new common fixed points theorem is given.The theorem let (f,A) and (g,B) are compatible self-mappings in X,and (f,A) and (g,B) are continuous mapping pair,fXBX,gXAX.If there exists non-negative real symmetric function Φ such that 1) Φ(x,x)=0,x∈X,Φ(x,y) is continuous;y∈X,Φ(x,y) is continuous; 2) x,y∈X,Φ(fx,gy)≤βΦ(Ax,By),0≤β<1; 3) x,y∈X, d(fx,gy)≤αmax｛d(Ax,By),d(Ax,fx),d(By,gy),12[d(Ax,gy)+d(By,fx)]｝+Φ(Ax,By),where 0≤α≤1,then ｛f,g,A,B｝ has the unique common fixed point.

关 键 词：完备度量空间 相容映射 公共不动点 

分 类 号：O177[理学—数学]