Please, are there any applications for the following fact.

Let $X$ be a complete, Hausdorff semi-metric space with a collection of semi-metrics $\{d_\alpha(\cdot,\cdot)\}_{\alpha\in A}.$ A mapping $f:X\to X$ is continuous and has the foloowing property. For any $\alpha\in A$ one can define an element $\gamma\in A$ and a number $c>0$ such that $$d_\gamma(f(x),f(y))\le d_\gamma(x,y)-cd_\alpha(x,y),\quad \forall x,y\in X.$$ Th. The mapping $f$ has a unique fixed point.