两个映射具有公共点的定理

THEOREM ABOUT COMMON POINT OF TWO MAPPINGS

本文得到了任一集合到完备度量空间中的两个映射具有公共点的定理，并在一类方程中得到应用。

Suppose S is an any set, and R is a metric space, A and B are two mappings from S to R. If it exists an element s in S, such that A(s)=B(s), then the s is called a common point of A and B.In this paper, it is proved that two mappings A and B from an any set S to a complete metric space (R, ρ), which B(S)A(S), and A(S) is a closed set in R, must have common points in S, if for any x,y∈S, the number α exists, 0≤α<1 followed ρ(B(x), B(y))≤αρ(A(x), A(y))let N= {s∈S|A(S)=B(s)}, then N= A-1(A(s))∩B-1(B(s)), s∈N. and also the common point is only one if the A (or B) is a injective mapping.