Strong Convergence to Common Fixed Points of Nonexpansive Mappings without Commutativity Assumption
نویسندگان
چکیده
for each x, y ∈ C. For a mapping T of C into itself, we denote by F(T) the set of fixed points of T . We also denote by N and R+ the set of positive integers and nonnegative real numbers, respectively. Baillon [1] proved the first nonlinear ergodic theorem. Let C be a nonempty bounded convex closed subset of a Hilbert spaceH and let T be a nonexpansive mapping of C into itself. Then, for an arbitrary x ∈ C, {(1/(n+1))∑i=0Tix}∞n=0 converges weakly to a fixed point of T . Wittmann [9] studied the following iteration scheme, which has first been considered by Halpern [3]:
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