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

Banaś, Józef; Sadarangani, Kishin

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 68, No. 2, 377-383 (2008).

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.

Keywords:

measure of noncompactness; monotone function; modulus of decrease; modulus of increase

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