CONVERGENCE OF MANN’S ALTERNATING PROJECTIONS IN CAT() SPACES

We study the convex feasibility problem in$\text{CAT}(\unicode[STIX]{x1D705})$spaces using Mann’s iterative projection method. To do this, we extend Mann’s projection method in normed spaces to$\text{CAT}(\unicode[STIX]{x1D705})$spaces with$\unicode[STIX]{x1D705}\geq 0$, and then we prove the$\unicode[STIX]{x1D6E5}$-convergence of the method. Furthermore, under certain regularity or compactness conditions on the convex closed sets, we prove the strong convergence of Mann’s alternating projection sequence in$\text{CAT}(\unicode[STIX]{x1D705})$spaces with$\unicode[STIX]{x1D705}\geq 0$.