Strong convergence for monotone bilevel equilibria with constraints of variational inequalities and fixed points using subgradient extragradient implicit rule

Abstract In a real Hilbert space, let GSVI and CFPP represent general system of variational inequalities common fixed point problem countable family nonexpansive mappings an asymptotically mapping, respectively. this paper, via new subgradient extragradient implicit rule, we introduce analyze two iterative algorithms for solving the monotone bilevel equilibrium (MBEP) with constraints, i.e., strongly over solution set another problem, CFPP. Some strong convergence results proposed are established under mild assumptions, they also applied finding GSVI, VIP, FPP, where VIP FPP stand inequality