摘要
设Ｘ为凸度量空间，具有性质（Ｃ）和（Ｅ），Ｋ是Ｘ的非空凸子集，Ｔ：Ｋ→２ｋ使得ｘ→ｄ（ｘ，Ｔｘ）是Ｌ．Ｓ．Ｃ．若ｉｎｆ｛ｄ（ｘ，Ｔｘ）；ｘ∈Ｋ｝＝０，且 ｘ，ｙ∈Ｋ，λ∈［０，１］，ｕ＝Ｗ（ｘ，ｙ，λ）（凸结构）有ｄ（ｕ，Ｔｕ）≤ （ｍａｘ｛ｄ（ｘ，Ｔｘ），ｄ（ｙ，Ｔｙ）｝），这里：Ｒ＋→Ｒ＋满足条件 （０）＝０，在０的右边不减，连续，则Ｔ在Ｋ上有不动点．给出了ｕ．Ｓ．ｃ．集值映射的不动点定理，推广了Ｔ．Ｈ．Ｃｈａｎｇ和Ｃ．Ｌ．Ｙｅｎ在Ｂａｎａｃｈ空间中的相应结果．
Let X be a convex metric space with properties(C)and(E).K be a nonempty convex subset of X. T:K→2￣x be a mapping such that the mapping x→d(x,Tx) is L. S.C. If inf{d(x,Tx):x∈K} =0 and for x,y in K,0≤λ≤1 u=ω(x,y,λ),and d (u, Tu)≤φ(max {d (x ,Tx), d (y,Ty)}) Where φ: R+→R+ is nondecreasing and continuous from the right at 0 with φ(0)=0,Then T has a fixed point on K. It get also the fixed point theorem for U. S. C. Set-valued mappings. They generalized the results of T. H. chang and C.L. Yen in Banach space.
出处
《东北师大学报（自然科学版）》
CAS
CSCD
1994年第4期13-16,共4页
Journal of Northeast Normal University(Natural Science Edition)
关键词
凸度量空间
集值映射
不动点
convex metric space
Set-valued mapping
fixed point
