D^*-度量空间广义弱压缩映射的不动点定理

Fixed point theorems for generalized weakly contractive maps in D^*-metric spaces

介绍了D^*-度量空间中的相关知识,并基于D^*-度量空间,将度量空间中与两种距离控制函数(ψ,ϕ)有关的广义弱压缩映射推广到D^*-度量空间,通过构造迭代序列,讨论了广义弱压缩条件下映射不动点的存在性和唯一性,给出了几个不动点定理,所得结果丰富了D^*-度量空间的不动点理论。

In this paper,we first introduce the notion of D^*-metric space and the related knowledge.Based on the D^*-metric space,we extend the generalized weakly contractive maps related to two kinds of distance control functions(ψ,ϕ)from metric space to the D^*-metric space,and discuss the existence and uniqueness of fixed point under generalized weakly contractive conditions by constructing iterative sequences.We also present several new fixed point theorems.The results enrich the fixed point theory of D^*-metric space.