1994•Proceedings of the Royal Society of Edinburgh Section A MathematicsRequires access
An ergodic theorem for asymptotically nonexpansive mappings
Manfred Krüppel, Jarosław Górnicki
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Abstract
The purpose of this paper is to prove the following (nonlinear) mean ergodic theorem: Let E be a uniformly convex Banach space, let C be a nonempty bounded closed convex subset of E and let T: C → C be an asymptotically nonexpansive mapping. If exists uniformly in r = 0, 1, 2,…, then the sequence {Tnx} is strongly almost-convergent to a fixed point y of T, that is, uniformly in i = 0, 1, 2, ….