## On some measures of noncompactness in the space of continuous functions.(English)Zbl 1134.46012

Summary: We consider some quantities in the space of continuous functions on a bounded interval, which are related to monotonicity of functions. Based on those quantities, we construct a few measures of noncompactness in the mentioned function space. Several properties of those measures are established; among others, it is shown that they are regular or “partly” regular measures and equivalent to the Hausdorff measure of noncompactness.

### MSC:

 46E15 Banach spaces of continuous, differentiable or analytic functions 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc.
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### References:

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