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arXiv · 2502.09634

Fixed point results and the Ekeland variational principle in vector $B$-metric spaces

Radu Precup·Andrei Stan
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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

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Radu Precup, Andrei Stan. 2025-02-07. Fixed point results and the Ekeland variational principle in vector $B$-metric spaces. https://arxiv.org/abs/2502.09634

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