On the problem of retracting balls onto their boundary (Q1864360)

As is well-known, the unit ball \(B(x)\) in a normed linear space may be retracted onto its boundary if and only if the space \(X\) is infinite dimensional. In their celebrated paper [Proc. Amer. Math. Soc. 88, 439-445 (1983; Zbl 0518.46010)], \textit{Y. Benyamini} and \textit{Y. Sternfeld} have shown that such retractions may always be chosen Lipschitz continuous. In this paper, the author studies the problem of finding estimates for the smallest possible Lipschitz constant.