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Duality for Best Approximation in Fuzzy Quasi-normed Spaces

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Abstract

In the study of the classical approximation and optimization problems, the dual method is a powerful tool. The present paper initiates the problems of the duality for best approximation in fuzzy quasi-normed spaces. It gives the characterization of the nearest points, and extends the well-known Arzela formula for the distance from a point to a hyperplane in a normed space to the case of a fuzzy quasi-normed space. The obtained notions and results show the validity of dual method in the study of best approximation for fuzzy quasi-normed spaces, and will play an important role in the research of this domain.

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Acknowledgements

The first author was supported by the National Natural Science Foundation of China (11971343).

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Authors and Affiliations

  1. School of Mathematical Science, Suzhou University of Science and Technology, Suzhou, 215009, Jiangsu, People’s Republic of China

    Jian-Rong Wu, He Liu & Hua Duan

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  1. Jian-Rong Wu
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  2. He Liu
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Correspondence to Jian-Rong Wu.

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Wu, JR., Liu, H. & Duan, H. Duality for Best Approximation in Fuzzy Quasi-normed Spaces. Int. J. Fuzzy Syst. 26, 333–343 (2024). https://doi.org/10.1007/s40815-023-01562-6

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  • DOI: https://doi.org/10.1007/s40815-023-01562-6

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