Solving generalized equilibrium with iterative techniques

In this paper, we propose a novel iterative algorithm for approximating solutions to generalized equilibrium problems and identifying common fixed point of a finite family of nonexpansive mappings in Hilbert spaces. Under suitable control conditions on the algorithmic parameters, we establish strong convergence of the generated sequence to a unique point that simultaneously solves the generalized equilibrium problem and lies in the intersection of the fixed point sets. This limit is further characterized as the unique solution to a corresponding variational inequality. The presented results extend and improve upon several recent contributions in the literature. Moreover, both the iterative scheme and the analytic techniques employed are of independent interest and may be applicable to broader classes of problems in nonlinear analysis.