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- W2440146281 abstract "We establish sharp estimates for the convergence rate of the Kranosel'skivi-Mann fixed point iteration in general normed spaces, and we use them to show that the asymptotic regularity bound recently proved in [11] (Israel Journal of Mathematics 199(2), 757-772, 2014) with constant $1/sqrt{pi}$ is sharp and cannot be improved. To this end we consider the recursive bounds introduced in [3] (Proceedings of the 2nd International Conference on Fixed Point Theory and Applications, World Scientific Press, London, 27-66, 1992) which we reinterpret in terms of a nested family of optimal transport problems. We show that these bounds are tight by building a nonexpansive map $T:[0,1]^{mathbb N}to[0,1]^{mathbb N}$ that attains them with equality, settling the main conjecture in [3]. The recursive bounds are in turn reinterpreted as absorption probabilities for an underlying Markov chain which is used to establish the tightness of the constant $1/sqrt{pi}$." @default.
- W2440146281 created "2016-06-24" @default.
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- W2440146281 date "2016-06-16" @default.
- W2440146281 modified "2023-09-27" @default.
- W2440146281 title "Sharp convergence rates for averaged nonexpansive maps" @default.
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