满足有理不等式四个映射的公共不动点定理

A common fixed point theorem for four mappings satisfying a rational inequality

研究了完备度量空间(X,d)中满足一个有理不等式的4个映射S、T、I和J的公共不动点的存在性和唯一性.进一步证明了两个映射{S,I}和{T,J}的公共不动点的存在性和唯一性,依据一个实例说明了定理的真实性与可靠性.其结果改进和推广了文[1]的结论,并指示了文[1]的例2错误的真正原因,与此同时对文[1]中例2进行了修改,给出了正确的满足文[1]中的有理不等式的4个映射S,T,I和J以及相关系数α,β和γ,使文[1]的例2的错误得以纠正.

In this article,the existence and uniqueness of common fixed point for mappings S,T,I and J（or two pairs of mappings,i.e.S and I,T and J） and satisfying a rational inequality in complete metric space are discussed.The truth and reliability of the theorem are illustrated with example.The obtained result extends and improves the corresponding conclusions in reference[1].And the exact reason for the false of example 2 in[1] is presented.At the same time,example 2 is corrected by presenting accuracy of four mappings satisfying the relational inequality in[1]and correlation coefficients,that is,α,β and γ.