Proper $k$-ball-contractive mappings in $C_b^m[0, + \infty)$
DOI:
https://doi.org/10.12775/TMNA.2021.017Keywords
Retraction, measure of noncompactness, $k$-ball-contraction, proper mappingAbstract
In this paper we deal with the Banach space $\C [0, + \infty)$ of all $m$-times continuously derivable, bounded with all derivatives up to the order $m$, real functions defined on $[0,+ \infty)$. We prove, for any $\eps > 0$, the existence of a new proper $k$-ball-contractive retraction with $k < 1+ \eps$ of the closed unit ball of the space onto its boundary, so that the Wo\'sko constant $W_\gamma (\C [0, + \infty))$ is equal to $1$.References
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Copyright (c) 2021 Diana Caponetti, Alessandro Trombetta, Giulio Trombetta
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