(untitled) (Communications in Mathematical Research, 2021)
In this paper, the iteration x_n+1 = α_ny + (1 − α_n)T^k(n)_i(n) x_n for a family of asymptotically nonexpansive mappings T_1, T_2, · · · , T_N is originally introduced in a uniformly convex Banach space. Motivated by recent papers, we prove that under suitable conditions the iteration scheme converges strongly to the nearest common fixed point of the family of asymptotically nonexpansive mappings. The results presented in this paper expand and improve corresponding ones from Hilbert spaces to uniformly convex Banach spaces, or from nonexpansive mappings to asymptotically nonexpansive mappings.