In this paper we deal with the Banach space C-b(m)[0,+infinity] of all m-times continuously derivable, bounded with all derivatives up to the order m, real functions defined on [0, +infinity). We prove, for any epsilon > 0, the existence of a new proper k-ball-contractive retraction with k < 1+epsilon of the closed unit ball of the space onto its boundary, so that the Wosko constant W-gamma(C-b(m)[0,+infinity]) is equal to 1.
Diana Caponetti, Alessandro Trombetta, Giulio Trombetta (2021). Proper $k$-ball-contractive mappings in $C_b^m[0, + infty)$. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 58(2), 609-639 [10.12775/TMNA.2021.017].
Proper $k$-ball-contractive mappings in $C_b^m[0, + infty)$
Diana Caponetti
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2021-12-01
Abstract
In this paper we deal with the Banach space C-b(m)[0,+infinity] of all m-times continuously derivable, bounded with all derivatives up to the order m, real functions defined on [0, +infinity). We prove, for any epsilon > 0, the existence of a new proper k-ball-contractive retraction with k < 1+epsilon of the closed unit ball of the space onto its boundary, so that the Wosko constant W-gamma(C-b(m)[0,+infinity]) is equal to 1.
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