一类特殊锥度量空间的度量化  

Metrizability of a type of special cone metric spaces

作　　者：王常春[1] 夏顺友[2] 罗东升[1] 

机构地区：[1]遵义师范学院数学与计算科学学院,贵州遵义563000 [2]贵州师范学院数学与计算机科学学院,贵州贵阳550018

出　　处：《辽宁工程技术大学学报（自然科学版）》2013年第6期848-851,共4页Journal of Liaoning Technical University (Natural Science)

基　　金：国家自然科学基金资助项目(11161008);贵州省科学技术基金资助项目(2012GZ71164)

摘　　要：为获得锥内部为空的特殊锥度量空间中序列的收敛性概念,以及这类锥度量空间的度量化,利用锥的正规性,通过锥中收敛于零元的向量序列定义了收敛序列、柯西序列和完备;为得到这类锥度量空间的度量化问题,利用控制锥度量的向量的范数的下确界定义了一种由锥度量诱导的实度量.证明了锥内部为空的锥度量空间中的序列收敛、柯西序列和相应的空间完备与诱导的实度量定义的序列收敛、柯西序列和相应的空间完备是等价的,即得到了锥内部为空的锥度量空间的一种度量化.作为应用,利用修改距离函数,证明了这种特殊锥度量空间中的一个不动点定理.In order to get the concept of convergence of sequence in the cone metric space with cone having no interiors and the metrizablity of this type of cone metric space, this paper defined convergence consequence, Cauchy sequence and completion by using the property of normal cone; further, defined a real metric induced by cone metric by norm of vector that controls the cone metric of cone metric space with cone having no interiors, then it is proved to be equivalent between convergence consequence, Cauchy sequence and complete defined by cone metric and convergence consequence, Cauchy sequence and complete defined by real metric induced by cone metric, and a type of metrizability for this type of cone metric space with cone having no interiors is derived. By using altering distance function, this study proved the theorem of a type of fixed point in the special type of cone metric space.

关 键 词：锥度量 锥度量空间 柯西序列 收敛 完备 不动点 正规锥 度量化 

分 类 号：O177.91[理学—数学]