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

Parin Chaipunya ()
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Parin Chaipunya: King Mongkut’s University of Technology Thonburi, Department of Mathematics, Faculty of Science

Chapter Chapter 6 in Advances in Metric Fixed Point Theory and Applications, 2021, pp 111-132 from Springer

Abstract: Abstract In this paper, we discuss the fixed point property for an infinite family of order-preserving mappings which satisfy the Lipschitz condition on comparable pairs. The underlying framework of our main results is a metric space of any global upper curvature bound $$\kappa \in \mathbb {R}$$ κ ∈ R , i.e., a $$\mathrm CAT(\kappa )$$ C A T ( κ ) space. In particular, we prove the existence of a fixed point for a nonexpansive semigroup on comparable pairs. Then, we propose and analyze two algorithms to approximate such a fixed point.

Keywords: $$\mathrm CAT(\kappa )$$ C A T ( κ ) space; Partially ordered metric space; Nonexpansive semigroup; Fixed point (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-33-6647-3_6

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DOI: 10.1007/978-981-33-6647-3_6

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