S Atsushiba, W Takahashi
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 57(1) 117-127, Feb, 1998 Peer-reviewed
Let C be a nonempty closed convex subset of a real Banach space E and let S,T be nonexpansive mappings of C into itself. In this paper, we consider the following iteration procedure of Mann's type for approximating common fixed points of two mappings S and T:
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where {alpha(N)} is a sequence in [0, 1]. Using some ideas in the nonlinear ergodic theory, we prove that the iterates converge weakly to a common fixed point of the nonexpansive mappings T and S in a uniformly convex Banach space which satisfies Opial's condition or whose norm is Frechet differentiable.