Ekeland's variational principle in fuzzy quasi-normed spaces

Wei Zhou; Jianrong Wu; Wei Zhou; Jianrong Wu

doi:10.3934/math.2022874

AIMS Mathematics

2022, Volume 7, Issue 9: 15982-15991. doi: 10.3934/math.2022874

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Research article

Ekeland's variational principle in fuzzy quasi-normed spaces

Wei Zhou ,
Jianrong Wu ^,

College of Mathematics Science, Suzhou University of Science and Technology, Suzhou, Jiangsu 215009, China

Received: 18 April 2022 Revised: 19 June 2022 Accepted: 23 June 2022 Published: 29 June 2022
MSC : 46S40, 58E30

Fuzzy quasi-normed space provides an ideal mathematical framework for studying asymmetric phenomena. In this paper, we prove a version of the Ekeland variational principle in fuzzy quasi-normed spaces and apply it to Caristi's fixed point theorem and Takahashi minimization theorem. Moreover, we prove the equivalence relations among these theorems.
- fuzzy quasi-norm,
- variational principle,
- fixed point theorem,
- minimization theorem
Citation: Wei Zhou, Jianrong Wu. Ekeland's variational principle in fuzzy quasi-normed spaces[J]. AIMS Mathematics, 2022, 7(9): 15982-15991. doi: 10.3934/math.2022874

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Abstract

Fuzzy quasi-normed space provides an ideal mathematical framework for studying asymmetric phenomena. In this paper, we prove a version of the Ekeland variational principle in fuzzy quasi-normed spaces and apply it to Caristi's fixed point theorem and Takahashi minimization theorem. Moreover, we prove the equivalence relations among these theorems.

References

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