Existence and Approximations for Order-Preserving Nonexpansive Semigroups over $\rm{CAT}(\kappa)$ Spaces

Parin Chaipunya

Existence and Approximations for Order-Preserving Nonexpansive Semigroups over $\rm{CAT}(\kappa)$ Spaces

Functional Analysis 2018-11-29 v1

Authors: Parin Chaipunya

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 $\kappa \in \mathbb{R}$ , i.e., a $\rm{CAT}(\kappa)$ 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.

Keywords

fixed point property order-preserving mappings nonexpansive semigroup cat(k) spaces lipschitz condition approximation algorithms comparable pairs

Cite

@article{arxiv.1811.11585,
  title  = {Existence and Approximations for Order-Preserving Nonexpansive Semigroups over $\rm{CAT}(\kappa)$ Spaces},
  author = {Parin Chaipunya},
  journal= {arXiv preprint arXiv:1811.11585},
  year   = {2018}
}

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