拓扑向量空间值锥度量空间的可度量化
一般拓扑
2011-09-23 v3
摘要
标量化方法是向量优化研究中的一个重要工具，因为向量优化问题的相应解可以通过求解标量优化问题来找到。Du (2010) [关于锥度量不动点理论及其等价性的注记，非线性分析 72 2259-2261] 应用此方法研究了广义锥度量空间中压缩映射的不动点定理的向量版本与通常意义下一般度量空间中不动点定理的标量版本之间的等价性。在本文中，我们发现由拓扑向量空间值锥度量诱导的拓扑与通过非线性标量化函数获得的度量诱导的拓扑一致，即任何拓扑向量空间值锥度量空间都是可度量化的。
引用
@article{arxiv.1007.3123,
title = {Metrizability of Topological Vector Space Valued Cone Metric Spaces},
author = {Huseyin Cakalli and Ayse Sonmez and Cigdem Genc},
journal= {arXiv preprint arXiv:1007.3123},
year = {2011}
}
备注
This paper has been withdrawn by the authors. We withdraw our paper due to the acceptance in the journal "Applied Mathematics Letters" with a different title. r has been withdrawn by the authors due to a