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DOI: 10.23952/cot.2027.7
Received November 24, 2025; Accepted March 11, 2026; Published online July 20, 2026
Abstract. In this paper, we introduce a proximal-type algorithm for solving equilibrium problems in Hilbert spaces, and prove the strong convergence of the generated sequence to a solution of the problem by assuming neither any monotonicity condition on the bifunction nor any weak continuity condition on its arguments. Moreover, assuming the boundedness of the generated sequence, we show that the solution set of the problem is nonempty and the sequence converges strongly to a solution of the problem.
How to Cite this Article:
B. Djafari Rouhani, V. Mohebbi, Approximation method for solving non-monotone equilibrium problems in Hilbert spaces, Commun. Optim. Theory 2027 (2027) 7.