Let k be at most 0, and let X a locally-finite CAT(k) polyhedral 2-complex X, each face with constant curvature k. E closed, rectifiably-connected subset of trivial first singular homology. We show that E, under the induced path metric, is complete space.

in this paper we derive convergence theorems for an -nonexpansive mappingof a nonempty closed and convex subset of a complete cat(0) space for sp-iterative process and thianwan's iterative process.

we prove a strong convergence theorem for the modified noor iterations‎ ‎in the framework of cat(0) spaces‎. ‎our results extend and improve the corresponding results of‎ ‎x‎. ‎qin‎, ‎y‎. ‎su and m‎. ‎shang‎, ‎t‎. ‎h‎. ‎kim and h‎. ‎k‎. ‎xu and s‎. ‎saejung‎ ‎and some others‎.

in this paper, several $delta$ and strong convergence theorems are established for the ishikawa iterations for nonexpansive mappings in the framework of cat(0) spaces. our results extend and improve the corresponding results