Equilibrium and Fixed Point Problems and Applications via Kirk–Cesàro Hybrid Iterative Schemes

Abstract

Kirk–Cesàro hybrid iterative schemes are developed in this study to approximate solutions of fixed point and equilibrium problems in real Hilbert spaces. The main novelty of this study is the development of new Kirk–Cesàro hybrid iterative schemes that combine the Kirk iterative structure, Cesàro meaning, and hybrid projection techniques for fixed point and equilibrium problems involving asymptotically nonexpansive mappings. Under appropriate conditions, norm convergence of the produced sequences toward the metric projection onto the fixed point set, as well as toward a joint solution of fixed point and equilibrium problems, is established. The derived results are further applied to convex optimization through an equivalent equilibrium formulation. The proposed framework may provide a useful theoretical basis for future applications in optimization and equilibrium modeling. Computational experiments and graphical illustrations are provided to demonstrate the convergence behavior of the proposed schemes.