Stability Properties for Multi-Valued Contractions in Complete Vector-Valued B -Metric Spaces

Ghiocel Moţ and Claudia Luminiţa Mihiţ ()
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Ghiocel Moţ: Department of Mathematics and Computer Science, “Aurel Vlaicu” University of Arad, Elena Drăgoi Street no. 2, 310330 Arad, Romania
Claudia Luminiţa Mihiţ: Department of Mathematics and Computer Science, “Aurel Vlaicu” University of Arad, Elena Drăgoi Street no. 2, 310330 Arad, Romania

Mathematics, 2025, vol. 13, issue 19, 1-9

Abstract: In this paper, we present some existence and stability results for the fixed point inclusion in the case of multi-valued self contractions, on a complete vector-valued B -metric space. Our main existence result for the fixed point problem extends to the multi-valued setting with a recent result obtained for the single-valued case. Moreover, data dependence on the operator perturbation of the fixed point set and some stability theorems (Ulam–Hyers stability, well-posedness and Ostrowski stability) are proved, in order to have a complete study of the fixed point inclusion.

Keywords: complete vector-valued B-metric space; fixed point; multi-valued contraction; Ulam–Hyers stability; Ostrowski stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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