In this paper, we introduce a new extension of the double controlled metric-type spaces, called double controlled metric-like spaces, by assuming that the “self-distance” may not be zero On the other hand, if the value of the metric is zero, then it has to be a “self-distance” (i.e., we replace $[\varsigma(g,h)=0 \Leftrightarrow g=h]$ by $[\varsigma(g,h)=0 \Rightarrow g=h]$ ). Using this new type of metric spaces, we generalize many results in the literature. We prove fixed point results along with examples illustrating our theorems. Also, we present double controlled metric-like spaces endowed with a graph along with an open question.

中文翻译：

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双控制度量空间

在本文中，我们通过假设“自距离”可能不为零，介绍了双控制度量类型空间的新扩展，称为双控制度量类似空间。为零，则它必须是“自距离”（即，我们将$ [\ varsigma（g，h）= 0 \ Leftrightarrow g = h] $替换为$ [\ varsigma（g，h）= 0 \ Rightarrow g = h] $）。使用这种新型的度量空间，我们可以在文献中概括许多结果。我们证明定点结果，并举例说明定理。此外，我们还提供了带有图和未解决问题的双控制度量式空间。