A product of strongly quasi-nonexpansive mappings in Hadamard spaces

2025/04/30 by W. Worapitpong, Worapitpong, Wiparat, Parin Chaipunya +5
Computer Science · Mathematics · #Optimization and Variational Analysis #Fixed Point Theorems Analysis #Advanced Optimization Algorithms Research

paper · pdf · doi:10.48550/arxiv.2504.21402

Abstract

In this paper, we prove that the product of strongly quasi-nonexpansive Δ-demiclosed mappings is also a strongly quasi-nonexpansive orbital Δ-demiclosed mapping in Hadamard spaces. Additionally, we establish the Δ-convergence theorem for approximating a common fixed point of infinite products of these mappings in Hadamard spaces. Our results have practical applications in convex function minimization, the minimization of the sum of finitely many convex functions, and solving the convex feasibility problem for finitely many sets in Hadamard spaces.

Citations

• On the Iterations of a Sequence of Strongly Quasi-nonexpansive Mappings\n with Applications
• The Asymptotic Behavior of the Composition of Firmly Nonexpansive Mappings
• Computing medians and means in Hadamard spaces
• The proximal point algorithm in metric spaces
• The proximal point algorithm in metric spaces
• Firmly nonexpansive mappings in classes of geodesic spaces
• Monotone Operators and the Proximal Point Algorithm

Related

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• Quasi-nonexpansive mappings with respect to orbits in Banach spaces and weak fixed point property
• On a useful lemma that relates quasi-nonexpansive and demicontractive mappings in Hilbert spaces