GENERAL IMPLICIT SUBGRADIENT EXTRAGRADIENT METHODS FOR MONOTONE BILEVEL EQUILIBRIUM PROBLEMS

In this paper, we introduce the general implicit subgradient extragradient method for solving the monotone bilevel equilibrium problem (MBEP) with a general system of variational inclusions (GSVI) and a common fixed-point problem of finitely many non -expansive mappings and a strictly pseudocontractive mapping (CFPP) constraints. The strong convergence result for the proposed algorithm is established under the monotonicity assumption of the cost bifunctions with Lipschitz-type continuous conditions recently presented by Mastroeni in the auxiliary problem principle, and also applied for finding a common solution of variational inequality, variational inclusion and fixed-point problems.