Let $X$ be a non-empty set. We say that an element $x\in X$ is a $\varphi$-fixed point of $T$, where $\varphi: X\to [0,\infty)$ and $T: X\to X$, if $x$ is a fixed point of $T$ and $\varphi(x)=0$. In this paper, we establish some existence results of $\varphi$-fixed points for various classes of operators in the case, where $X$ is endowed with a metric $d$. The obtained results are used to deduce some fixed point theorems in the case where $X$ is endowed with a partial metric $p$.
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机译：设$ X $为非空集。我们说X $中的元素$ x \是$ T $的$ \ varphi $不动点，其中$ \ varphi：X \至[0，\ infty）$和$ T：X \ to X $，如果$ x $是$ T $的固定点并且$ \ varphi（x）= 0 $。在本文中，我们为$ X $被赋予度量$ d $的情况下的各个类别的运算符建立了$ \ varphi $-固定点的存在性结果。在$ X $被赋予部分度量$ p $的情况下，所获得的结果用于推导某些不动点定理。
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