On properties of contractions and nonexpansive mappings on spherical caps in Hilbert spaces
Krzysztof Bolibok, Mariusz Szczepanik · Fixed Point Theory · 2017
Let H be an at least two-dimensional real Hilbert space with the unit sphere S H . For [-1, 1] and n S H we define an (, n)-spherical cap by S,n = {x S H : x, n }. We show that the distance between the set of contractions T : S,n S,n and the identity mapping is positive iff < 0. We also study the fixed point property and the minimal displacement problem in this setting for nonexpansive mappings.