Convergences of Alternating Projections in CAT($κ$) Spaces

Abstract

We establish the asymptotic regularity and the $Δ$-convergence of the sequence constructed by the alternating projections to closed convex sets in a CAT($κ$) space with $κ> 0$. Furthermore, the strong convergence of the alternating von Neumann sequence is presented under certain regularity or compactness.

15 pages