Convergences of Alternating Projections in $$\\mathrm{CAT}(\\kappa )$$ CAT ( κ ) Spaces

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