Existence and stability theorems in vector-valued metric spaces for fixed point and coincidence point problems governed by multi-valued weak contractions

Adrian Petruşel () and Gabriela Petruşel ()
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Adrian Petruşel: Babeş-Bolyai University
Gabriela Petruşel: Academy of Romanian Scientists

Journal of Optimization Theory and Applications, 2025, vol. 206, issue 3, No 20, 15 pages

Abstract: Abstract In this work, in the setting of a vector-valued metric space X, the fixed point inclusion $$x\in G(x), x\in X$$ x ∈ G ( x ) , x ∈ X governed by a multi-valued operator $$G:X\multimap X$$ G : X ⊸ X satisfying a weak contraction type condition on its graph is studied. Some stability results are obtained and the coincidence point problem involving two multi-valued operators is also studied. The best proximity point problem in vector-valued metric spaces is finally discussed.

Keywords: Vector-valued metric space; Fixed point; Coincidence point; Weak multi-valued contraction; Stability properties; 47H10; 49J53; 54H25 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02758-6

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