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Volume 4, Issue 3, 1 December 2022, Pages 293-310
Abstract. We present a self-contained analysis of a particular family of metrics over the set of non-negative integers. We show that these metrics, which are defined through a nested sequence of optimal transport problems, provide tight estimates for general Krasnosel’skii-Mann fixed point iterations for non-expansive maps. We also describe some of their special properties, including their monotonicity and the so-called convex quadrangle inequality that yields a greedy algorithm for computing them efficiently.
How to Cite this Article:
Mario Bravo, Thierry Champion, Roberto Cominetti, Universal bounds for fixed point iterations via optimal transport metrics, Appl. Set-Valued Anal. Optim. 4 (2022), 293-310.