Optimal retraction problem for proper $k$-ball-contractive mappings in $C^m [0,1]$

Diana Caponetti, Alessandro Trombetta, Giulio Trombetta

DOI: http://dx.doi.org/10.12775/TMNA.2018.041


In this paper for any $\eps > 0$ we construct a new proper $k$-ball-contractive retraction of the closed unit ball of the Banach space $C^m [0,1]$ onto its boundary with $k < 1+ \eps$, so that the Wo\'sko constant $W_\gamma (C^m [0,1])$ is equal to $1$.


Retraction; measure of noncompactness; proper mapping

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