Firmly nonexpansive mappings in classes of geodesic spaces

Ariza-Ruiz, David; Leuştean, Laurenţiu; López-Acedo, Genaro

doi:10.1090/S0002-9947-2014-05968-0

Firmly nonexpansive mappings in classes of geodesic spaces
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by David Ariza-Ruiz, Laurenţiu Leuştean and Genaro López-Acedo PDF

Trans. Amer. Math. Soc. 366 (2014), 4299-4322 Request permission

Abstract:

Firmly nonexpansive mappings play an important role in metric fixed point theory and optimization due to their correspondence with maximal monotone operators. In this paper we do a thorough study of fixed point theory and the asymptotic behaviour of Picard iterates of these mappings in different classes of geodesic spaces, such as (uniformly convex) $W$-hyperbolic spaces, Busemann spaces and CAT(0) spaces. Furthermore, we apply methods of proof mining to obtain effective rates of asymptotic regularity for the Picard iterations.

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