DOI: 10.24193/fpt-ro.2025.1.03

Authors: Arian Bërdëllima and Gabriele Steidl

Abstract: This paper introduces the concept of quasi α-firmly nonexpansive mappings in Wasserstein spaces over ℝ^d and analyzes properties of these mappings. We prove that for quasi α-firmly nonexpansive mappings satisfying a certain quadratic growth condition, the fixed point iterations converge in the narrow topology. As a byproduct, we will get the known convergence of the proximal point algorithm in Wasserstein spaces. We apply our results to show for the first time that cyclic proximal point algorithms for minimizing the sum of certain functionals on Wasserstein spaces converge under appropriate assumptions.

Key Words and Phrases: Quasi α-firmly nonexpansive mappings, Wasserstein spaces, fixed point, cyclic proximal algorithm, push-forward operator, optimal transport.

2010 Mathematics Subject Classification: 46T99, 47H10, 47J25, 28A33.

Published on-line: February 1st, 2025.

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