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An ergodic theorem for asymptotically nonexpansive mappings
Published online by Cambridge University Press: 14 November 2011
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, ….
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 124 , Issue 1 , 1994 , pp. 23 - 31
- Copyright
- Copyright © Royal Society of Edinburgh 1994