Abstract

It is shown in this paper that the notion of α-dense curve in a bounded set of a metric space produces a degree of nondensifiability ϕd\phi_d which extended to convex hulls of bounded sets in a Banach space generates a measure of noncompactness (briefly MNC) Φ that we will call degree of convex nondensifiability. We also prove that Φ dominates any other MNC and, in particular, dominates the MNC of Hausdorff of the best possible form in infinite dimensional Banach spaces.

Author information

Contact details are reproduced from the original publication and may be historical.

Gaspar Mora Martinez

Dpto. Analisis Matematico, Universidad de Alicante, Ap. de Correos 99, 03080 Alicante, Spain

gaspar.mora@ua.es

Keywords

  • alpha-dense curves
  • degree of nondensifiability
  • degree of convex nondensifiability
  • measures of noncompactness

Mathematics Subject Classification

47H08, 46B20

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Suggested citation

G. Garcia Macias, G. Mora Martinez. “The Degree of Convex Nondensifiability in Banach Spaces.” Journal of Convex Analysis 22 (2015), No. 3, 871–888. https://doi.org/10.68381/jca22045

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Published by Heldermann Verlag, 2015. Rights now held by Banach Press LLC.