锥度量空间与相关不动点定理研究

Cone Metric Space and the Study of Fixed Point Theorem

在引进锥的概念下,运用锥诱导出的半序关系,研究锥度量空间中的收敛性、完备性和相关映射的不动点问题.以半序关系下的Banach压缩不动点定理为工具,获得单值映射的不动点和两个单值映射的公共不动点的存在性及唯一性,推广度量空间中的相关不动点定理.

By introducing the concept of cone and using the partial order relation induced by cone, the con- vergence, completeness and fixed point problems of correlation mapping in cone metric space are studied. By using the Banach contraction fixed point theorem under the partial order relation as a tool, the existence and uniqueness of the fixed points of single-valued mappings and the common fixed points of two single-valued mappings are obtained, and the related fixed point theorems in metric spaces are generalized.