A New Iterative Method for Common Fixed Points of a Finite Family of Nonexpansive Mappings
Suwicha Imnang, Suthep Suantai · International Journal of Mathematics and Mathematical Sciences · 2009
Let X be a real uniformly convex Banach space and C a closed convex nonempty subset of X. Let be a finite family of nonexpansive self‐mappings of C. For a given x1 ∈ C, let {xn} and , i = 1, 2, …, r, be sequences defined , where for all j ∈ {1, 2, …, r}, n ∈ ℕ and i = 1, 2, …, j. In this paper, weak and strong convergence theorems of the sequence {xn} to a common fixed point of a finite family of nonexpansive mappings Ti (i = 1, 2, …, r) are established under some certain control conditions.