实线性锥距离空间和不动点定理

贺飞, 丘京辉

数学学报 ›› 2014, Vol. 57 ›› Issue (1) : 171-180.

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PDF(451 KB)
数学学报 ›› 2014, Vol. 57 ›› Issue (1) : 171-180. DOI: 10.12386/A2014sxxb0017
论文

实线性锥距离空间和不动点定理

    贺飞1,2, 丘京辉1
作者信息 +

Real Vector Cone Metric Space and Fixed Point Theorems

    Fei HE1,2, Jing Hui QIU1
Author information +
文章历史 +

摘要

给出了实线性锥距离空间的概念,其中锥距离取值到没有拓扑结构的实线性空间,并在实线性锥距离空间中建立了几个新的不动点定理.利用非线性标量化函数证明了这些不动点定理与距离空间中相应形式的不动点定理等价.我们的结果改进了锥距离空间中的一些现有不动点定理.

Abstract

We introduce real vector cone metric spaces, where cone metric is the mapping on a real vector space without topological structures. We also prove some new fixed point theorems in real vector cone metric spaces. By using nonlinear scalarization functions, we establish the equivalence between these and some other fixed point results in metric and in real vector cone metric spaces. Our results improve and generalize some results from the literature.

关键词

不动点定理 / 距离空间 / 实线性锥距离空间

Key words

fixed point theorem / metric space / real vector cone metric space

引用本文

导出引用
贺飞, 丘京辉. 实线性锥距离空间和不动点定理. 数学学报, 2014, 57(1): 171-180 https://doi.org/10.12386/A2014sxxb0017
Fei HE, Jing Hui QIU. Real Vector Cone Metric Space and Fixed Point Theorems. Acta Mathematica Sinica, Chinese Series, 2014, 57(1): 171-180 https://doi.org/10.12386/A2014sxxb0017

参考文献

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基金

国家自然科学基金资助项目(10871141);内蒙古自治区高等学校科学研究项目(NJZZ13019)
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