Existence and Approximations for Order-Preserving Nonexpansive Semigroups over \rmCAT(κ) Spaces

2018/11/28 by Parin Chaipunya, Chaipunya, Parin
Computer Science · Mathematics · #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1811.11585

openalex publication_date 2018/11/28 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

In this paper, we discuss the fixed point property for an infinite family of order-preserving mappings which satisfy the Lipschitzian condition on comparable pairs. The underlying framework of our main results is a metric space of any global upper curvature bound κ∈ ℝ, i.e., a \rmCAT(κ) space. In particular, we prove the existence of a fixed point for a nonexpasive semigroup on comparable pairs. Then, we propose and analyze two algorithms to approximate such a fixed point.

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