FIXED POINT ITERATIONS IN HYPERBOLIC SPACES

We give a simple proof of the well-known fixed point theorem of Goebel and Kirk [A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 35(1972), 171-174] in the setting of a hyperbolic space. We also obtain Delta-convergence and strong convergence theorems of one-step iteations of two strongly asymptotically (quasi-) nonexpansive mappings in this setting. Our results extend and improve many results in the current literature.