Bulletin of the
Korean Mathematical Society BKMS

We introduce an iteration scheme for approximating common fixed points of two mappings. On one hand, it extends a scheme due to Agarwal et al. [2] to the case of two mappings while on the other hand, it is faster than both the Ishikawa type scheme and the one studied by Yao and Chen [18] for the purpose in some sense. Using this scheme, we prove some weak and strong convergence results for approximating common fixed points of two nonexpansive self mappings. We also outline the proofs of these results to the case of nonexpansive nonself mappings.

Keywords: iteration scheme, nonexpansive self mapping, nonexpansive nonself mapping, rate of convergence, common fixed point, the condition ($A^{\prime }$), weak and strong convergence

MSC numbers: 47H09, 47H10