Geodesic
The Degree of Convex Nondensifiability in Banach Spaces
Journal of convex analysis, Tome 22 (2015) no. 3, pp. 871-888
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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 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.
Classification : 47H08, 46B20
Mots-clés : alpha-dense curves, degree of nondensifiability, degree of convex nondensifiability, measures of noncompactness 
@article{JCA_2015_22_3_JCA_2015_22_3_a15,
     author = {G. Garcia Macias and G. Mora Martinez},
     title = {The {Degree} of {Convex} {Nondensifiability} in {Banach} {Spaces}},
     journal = {Journal of convex analysis},
     pages = {871--888},
     year = {2015},
     volume = {22},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2015_22_3_JCA_2015_22_3_a15/}
}
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G. Garcia Macias; G. Mora Martinez. The Degree of Convex Nondensifiability in Banach Spaces. Journal of convex analysis, Tome 22 (2015) no. 3, pp. 871-888. http://geodesic.mathdoc.fr/item/JCA_2015_22_3_JCA_2015_22_3_a15/