DOI: 10.24193/fpt-ro.2023.1.05

Authors: Lu-Chuan Ceng, Adrian Petrușel, X. Qin and J.C. Yao

Abstract: In a real Hilbert space, let the GSVI and CFPP represent a general system of variational inclusions and a common fixed point problem of countable nonexpansive mappings and an asymptotically nonexpansive mapping, respectively. In this paper, via a new inertial subgradient extragradient rule we introduce and analyze two iterative algorithms for solving the monotone bilevel equilibrium problem (MBEP) with the GSVI and CFPP as constraints. Some strong convergence theorems for the proposed algorithms are established under some mild assumptions. Our results improve and extend some corresponding results in the earlier and very recent literature.

Key Words and Phrases: Inertial subgradient extragradient rule, monotone bilevel equilibrium problem, general system of variational inclusions, asymptotically nonexpansive mapping, countable nonexpansive mappings.

2010 Mathematics Subject Classification: 49J30, 47H09, 47H10, 47J20.

Published on-line: February 1st, 2023.

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