论文标题
一种概括度量功能的新方法
A new approach to generalize metric functions
论文作者
论文摘要
S-Metric和B-inetric空间是可迁移的，但是仍然不可能获得相关度量功能的明确形式。为了克服这一点，通过对三角形不等式进行合适的修改及其属性非常类似于公制功能，$ ϕ $ metric的概念是开发出来的。结果表明，人们可以轻松地从现有的广义距离函数（例如S-金属，B-Metric等）中构造一个$ ϕ $ metric。这些功能是$ ϕ $ - 超元素。这些度量空间上序列的收敛与相应的$ ϕ $ metric空间相同。因此，与指标不同，相关的$ ϕ $ metric可以很容易地构造，并且$ ϕ $ - metric函数可能会基本上起着公制功能的作用。同样，还研究了$ ϕ $ - metric空间的结构，并建立了一些固定点定理。
S-metric and b-metric spaces are metrizable, but it is still quite impossible to get an explicit form of the concerned metric function. To overcome this, the notion of $ϕ$-metric is developed by making a suitable modification in triangle inequality and its properties are pretty similar to metric function. It is shown that one can easily construct a $ϕ$-metric from existing generalized distance functions like S-metric, b-metric, etc. and those are $ϕ$-metrizable. The convergence of sequence on those metric spaces is identical to the respective induced $ϕ$-metric spaces. So, unlike metrics, concerned $ϕ$-metric can be easily constructed and $ϕ$-metric functions may play the role of metric functions substantially. Also, the structure of $ϕ$-metric spaces is studied and some fixed point theorems are established.
