LAUSR

For two nonempty, closed, bounded and convex subsets A and B of a uniformly convex Banach space X consider a mapping $$T:(A \times B) \cup (B \times A) \rightarrow A \cup B$$ T : ( A × B ) ∪ ( B × A ) → A ∪ B satisfying $$T(A,B) \subset B$$ T ( A , B ) ⊂ B and $$T(B, A) \subset A$$ T ( B , A ) ⊂ A . In this paper the existence of a coupled best proximity point is established when T is considered to be a p-cyclic contraction mapping and a p-cyclic nonexpansive mapping. The Ulam–Hyers stability of the best proximity point problem is also studied. Moreover, we establish the existence of a solution of the bi-equilibrium problem in Hilbert spaces as an application.