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DOI: 10.23952/cot.2026.11
Received October 6, 2024; Accepted February 17, 2025; Published online January 28, 2026
Abstract. In this paper, we study an inexact version of the proximal point algorithm for solving quasi-equilibrium problems in Banach spaces. We show that the sequence generated by the algorithm converges strongly to a solution of the problem. Our algorithm is new and requires fewer iterative steps than our previous algorithms in [D. Rouhani, V. Mohebbi, Extragradient methods for quasi-equilibrium problems in Banach spaces, J. Aust. Math. Soc. 112 (2022) 90–114] and [D. Rouhani, V. Mohebbi, Proximal point method for quasi-equilibrium problems in Banach spaces, Numer. Funct. Anal. Optim. 41 (2020) 1007–1026]. Finally, we present some applications and numerical experiments of our results.
How to Cite this Article:
B. Djafari Rouhani, V. Mohebbi, On the approximation of solutions of quasi-equilibrium problems with errors, Commun. Optim. Theory 2026 (2026) 11.