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Examples of proper k-ball contractive retractions in F-normed spaces

Diana CaponettiAlessandro TrombettaG. Trombetta

subject

Discrete mathematicsPure mathematicsApplied Mathematicsρ-Near retractionk-Ball contractionRegular F-normed ideal spaceRetractionHausdorff measure of noncompactnessHausdorff measureBall (mathematics)Hausdorff measure of noncompactneF-spaceAnalysisNormed vector spaceMathematics

description

Abstract Assume X is an infinite dimensional F -normed space and let r be a positive number such that the closed ball B r ( X ) of radius r is properly contained in X . The main aim of this paper is to give examples of regular F -normed ideal spaces in which there is a 1-ball or a ( 1 + e ) -ball contractive retraction of B r ( X ) onto its boundary with positive lower Hausdorff measure of noncompactness. The examples are based on the abstract results of the paper, obtained under suitable hypotheses on X .

yearjournalcountryeditionlanguage
2007-11-01Journal of Mathematical Analysis and Applications
10.1016/j.jmaa.2007.02.036http://dx.doi.org/10.1016/j.jmaa.2007.02.036