t-Semi-Lipschitz functions and t-best approximation in fuzzy quasi-metric spaces

Jian-Rong Wu; Lei Hua; Fei Yang; Jian-Rong Wu; Lei Hua; Fei Yang

doi:10.3934/math.20261274

AIMS Mathematics

2026, Volume 11, Issue 10: 32409-32429. doi: 10.3934/math.20261274

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Research article

t-Semi-Lipschitz functions and t-best approximation in fuzzy quasi-metric spaces

Department of Basic Courses, Wuxi Taihu University, Wuxi, Jiangsu 214064, China

Received: 15 May 2026 Revised: 13 August 2026 Accepted: 03 September 2026 Published: 08 October 2026
MSC : 41A50, 41A65, 46S40

In this paper, we introduced the concept of a t-semi-Lipschitz function defined on a fuzzy quasi-metric space with values in a fuzzy quasi-normed space. We showed that the set of such functions vanishing at a fixed point forms a quasi-normed cone. By means of t-semi-Lipschitz functions, we characterized the t-nearest points to a point from a subset and provided a formula for the corresponding nearest distance, specifically within an important subclass of fuzzy quasi-metric spaces known as fuzzy quasi-ultrametric spaces. The obtained results provide powerful tools for the qualitative description and quantitative analysis of best approximation problems in fuzzy environments.
- semi-Lipschitz function,
- fuzzy quasi-metric space,
- fuzzy quasi-normed space,
- best approximation
Citation: Jian-Rong Wu, Lei Hua, Fei Yang. t-Semi-Lipschitz functions and t-best approximation in fuzzy quasi-metric spaces[J]. AIMS Mathematics, 2026, 11(10): 32409-32429. doi: 10.3934/math.20261274

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Abstract

In this paper, we introduced the concept of a t-semi-Lipschitz function defined on a fuzzy quasi-metric space with values in a fuzzy quasi-normed space. We showed that the set of such functions vanishing at a fixed point forms a quasi-normed cone. By means of t-semi-Lipschitz functions, we characterized the t-nearest points to a point from a subset and provided a formula for the corresponding nearest distance, specifically within an important subclass of fuzzy quasi-metric spaces known as fuzzy quasi-ultrametric spaces. The obtained results provide powerful tools for the qualitative description and quantitative analysis of best approximation problems in fuzzy environments.

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