An algorithm for quasiconvex equilibrium problems and asymptotically nonexpansive mappings: application to a Walras model with implicit supply–demand

We propose a normal subgradient projection algorithm for approximating a solution of equilibrium problems involving quasiconvex para-pseudomonotone bifunctions, which is also a fixed point of an asymptotically nonexpansive mapping. The proposed algorithm is a combination between a projection one for the equilibrium problem and the Ishikawa iteration scheme for the fixed point. Convergence of the algorithm is proved without any Lipschitz type condition for the bifunction. Applications to a modified Walras equilibrium model with implicit supply and demand are discussed. © 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.