Set-contractions and ball-contractions in some classes of spaces
Let X be a Banach space, D an arbitrary subset of X, and T: \(D\to X\) a set condensing mapping. The main result of this paper states that: If \(X=\ell^ p\), \(1\leq p\leq +\infty\), then T is ball-condensing. It is also shown that the above result does not hold for \(X=L^ p[0,1]\), \(1\leq p<+\infty\), \(p\neq 2\).
scientific article; zbMATH DE number 4113349