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

In: Advances in Metric Fixed Point Theory and Applications

Author

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  • Parin Chaipunya

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

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.

Suggested Citation

  • Parin Chaipunya, 2021. "Existence and Approximations for Order-Preserving Nonexpansive Semigroups over $$\mathrm{CAT}(\kappa )$$ CAT ( κ ) Spaces," Springer Books, in: Yeol Je Cho & Mohamed Jleli & Mohammad Mursaleen & Bessem Samet & Calogero Vetro (ed.), Advances in Metric Fixed Point Theory and Applications, chapter 0, pages 111-132, Springer.
    • Handle: RePEc:spr:sprchp:978-981-33-6647-3_6
    DOI: 10.1007/978-981-33-6647-3_6
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