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Post Reopened by Pietro Majer, joro, Gil Kalai, Andrey Rekalo, Benjamin Steinberg
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Stefan Kohl ♦
Stefan Kohl ♦
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"contraction "Contraction mapping principle"

Please, areAre there any applications forof the following fact.?:

Let $X$ be a complete, Hausdorff semisemi-metric space with a collection of semi-metrics $\{d_\alpha(\cdot,\cdot)\}_{\alpha\in A}.$ A mapping Further let $f:X\to X$ isbe a continuous and has the foloowing property.mapping such that Forfor any $\alpha\in A$ one can define an element$\alpha \in A$ there is a $\gamma\in A$$\gamma \in A$ and a number $c>0$$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 mappingThen $f$ has a unique fixed point.

"contraction mapping principle"

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.

"Contraction mapping principle"

Are there any applications of the following fact?:

Let $X$ be a complete Hausdorff semi-metric space with a collection of semi-metrics $\{d_\alpha(\cdot,\cdot)\}_{\alpha\in A}.$ Further let $f:X\to X$ be a continuous mapping such that for any $\alpha \in A$ there is a $\gamma \in A$ and a number $c > 0$ such that $$d_\gamma(f(x),f(y))\le d_\gamma(x,y)-cd_\alpha(x,y),\quad \forall x,y\in X.$$ Then $f$ has a unique fixed point.

Post Closed as "Not suitable for this site" by Andrés E. Caicedo, Nik Weaver, Andy Putman, j.c., Andrey Rekalo
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cuckoo
cuckoo
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"contraction mapping principle"

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.