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Volume 14
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Article

Fixed-Point Results and the Ekeland Variational Principle in Vector B-Metric Spaces

by
Radu Precup
1,2,* and
Andrei Stan
2,3
1
Faculty of Mathematics and Computer Science and Institute of Advanced Studies in Science and Technology, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania
2
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, P.O. Box 68-1, 400110 Cluj-Napoca, Romania
3
Department of Mathematics, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania
*
Author to whom correspondence should be addressed.
Axioms 2025, 14(4), 250; https://doi.org/10.3390/axioms14040250
Submission received: 9 February 2025 / Revised: 24 March 2025 / Accepted: 25 March 2025 / Published: 26 March 2025
(This article belongs to the Special Issue Fixed-Point Theory and Its Related Topics, 5th Edition)
Versions Notes

Abstract

In this paper, we extend the concept of b-metric spaces to the vectorial case, where the distance is vector-valued, and the constant in the triangle inequality axiom is replaced by a matrix. For such spaces, we establish results analogous to those in the b-metric setting: fixed-point theorems, stability results, and a variant of Ekeland’s variational principle. As a consequence, we also derive a variant of Caristi’s fixed-point theorem.
Keywords: triangle inequality axiom; b-metric space; variational principle; fixed point triangle inequality axiom; b-metric space; variational principle; fixed point

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MDPI and ACS Style

Precup, R.; Stan, A. Fixed-Point Results and the Ekeland Variational Principle in Vector B-Metric Spaces. Axioms 2025, 14, 250. https://doi.org/10.3390/axioms14040250

AMA Style

Precup R, Stan A. Fixed-Point Results and the Ekeland Variational Principle in Vector B-Metric Spaces. Axioms. 2025; 14(4):250. https://doi.org/10.3390/axioms14040250

Chicago/Turabian Style

Precup, Radu, and Andrei Stan. 2025. "Fixed-Point Results and the Ekeland Variational Principle in Vector B-Metric Spaces" Axioms 14, no. 4: 250. https://doi.org/10.3390/axioms14040250

APA Style

Precup, R., & Stan, A. (2025). Fixed-Point Results and the Ekeland Variational Principle in Vector B-Metric Spaces. Axioms, 14(4), 250. https://doi.org/10.3390/axioms14040250

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