Convergences of Alternating Projections in CAT($\kappa$) Spaces

Abstract

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