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Research Article | Open Access

The properties of generalized John domains in metric spaces

Hongjun Liu( ), Fang Yan, Ling Xia
School of Mathematical Sciences, Guizhou Normal University, Guiyang, 550025, China
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Abstract

In this paper, we studied the properties of generalized John domains in metric space. We prove that a domain D is a φ-John domain if, and only if, D ∖ P is a φ ′ -John domain, where P is a subset of D containing finitely many points of D. Meanwhile, we also showed that the union of φ-John domains is a φ ″ -John domain in metric space.

Keywords

Generalized John domainuniform domaindecomposition propertyunionquasiconvex domain
CLC number: 30C20, 30C65

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AIMS Mathematics
Volume 9 Issue 6,
May 2024
Pages 15875-15890
DOI: 10.3934/math.2024767

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Cite this article:
Liu H, Yan F, Xia L. The properties of generalized John domains in metric spaces. AIMS Mathematics, 2024, 9(6): 15875-15890. https://doi.org/10.3934/math.2024767

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Received: 19 February 2024
Revised: 27 March 2024
Accepted: 18 April 2024
Published: 06 May 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)