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Variational principles using a non-symmetric non-triangular distance.

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Title: Variational principles using a non-symmetric non-triangular distance.
Authors: Boonyam, Natthaya1 (AUTHOR) natthaya.b@mail.kmutt.ac.th, Chaipunya, Parin1,2 (AUTHOR) parin.cha@kmutt.ac.th, Kumam, Poom1,2 (AUTHOR) poom.kum@kmutt.ac.th
Source: Fixed Point Theory & Algorithms for Sciences & Engineering. 1/22/2026, Vol. 2026 Issue 1, p1-14. 14p.
Subjects: Variational principles, Fixed point theory, Equilibrium
Abstract: We consider Borwein-Preiss and Ekeland variational principles using a distance function that neither is symmetric nor enjoy the triangular inequality. All the given results rely exclusively on the convergence and continuity behaviors induced synthetically by the distance function itself without any topological implications. At the end of the paper, we also present two applications; the Caristi fixed point theorem and an existence theorem for equilibrium problems. [ABSTRACT FROM AUTHOR]
Copyright of Fixed Point Theory & Algorithms for Sciences & Engineering is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Variational principles using a non-symmetric non-triangular distance.
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  Data: We consider Borwein-Preiss and Ekeland variational principles using a distance function that neither is symmetric nor enjoy the triangular inequality. All the given results rely exclusively on the convergence and continuity behaviors induced synthetically by the distance function itself without any topological implications. At the end of the paper, we also present two applications; the Caristi fixed point theorem and an existence theorem for equilibrium problems. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Fixed Point Theory & Algorithms for Sciences & Engineering is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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