Firmly nonexpansive mappings in classes of geodesic spaces

By David Ariza-Ruiz, Laurentiu Leustean, Genaro López-Acedo. 2012

146 citations recorded by the source corpus.

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. MSC: Primary: 47H09, 47H10, 53C22; Secondary: 03F10, 47H05, 90C25, 52A41.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/0d6f31c3f09cbb1f315cd8736dc3c813a4c9d489

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In Computational Theory and Mathematics

1. Zuly Salinas
2. Simeon Reich
3. Dang Van Hieu
4. Duong Viet Thong
5. Aviv Gibali
6. Yekini Shehu
7. Satit Saejung
8. Oluwatosin Temitope Mewomo

In Geometry and Topology

1. Zuly Salinas
2. Simeon Reich

In Numerical Analysis

1. Zuly Salinas
2. Simeon Reich
3. Dang Van Hieu
4. Duong Viet Thong
5. Yekini Shehu
6. Aviv Gibali
7. Oluwatosin Temitope Mewomo
8. Satit Saejung

Citations in the corpus

• Weak convergence of infinite products of operators in Hadamard spaces (2016, background): “Given t ∈ [0, 1], we write C(T1, T2; 1− t, t) := (1− t)T1 ⊕ tT2.”