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 in equality 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.
Authors
Radu Precup
Faculty of Mathematics and Computer Science and Institute of Advanced Studies in Science and Technology, Babes-Bolyai, University, Cluj-Napoca, Romania
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Romania
Andrei Stan
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Romania
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
Keywords
tiangle inequality axiom; b-metric space; variational principle; fixed point
Paper coordinates
R. Precup, A. Stan, Fixed Point Results and the Ekeland Variational Principle in Vector B-Metric Spaces, Preprints.org., 10.20944/preprints202502.0815.v1
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