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What happens with the Banach contraction principle in quasi metric spaces ? Here's the definition of a quasi metric space Quasi metric and here's the Banach contraction principle for metric spaces Banach fixed point theorem ( The difference between a metric and a quasi-metric is that a quasi-metric does not possess the symmetry axiom ).

user10354138
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ursuv2
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  • You need to define which version of completeness you are using for quasimetrics. – user10354138 Jun 18 '19 at 22:50
  • I just wanna know what happens with the triangle inequality in a quasi metric space.,a inequality with $d(\xi,x_n)$ where $\xi$ is the fixed point of a function. I'm sorry, my english doesn't help me too much, hope you understand. – ursuv2 Jun 18 '19 at 22:58
  • That part is word-for-word the same as metric space case. You don't need to use symmetry in the metric, so it works for quasimetric. – user10354138 Jun 18 '19 at 23:07
  • You mean there's not difference between metric space case and quasi metric space case ? I mean , if the symmetry doesn't count there, do we have the same condition to estimate the error when we solve an equation as metric spaces ? $$ d(\xi,x_n)\leq \displaystyle{{C^n}\over{1-C}}d(x_0,x_1)$$ where $0\leq C<1$ and $\xi$ the fixed point. – ursuv2 Jun 18 '19 at 23:13

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