The hybrid steepest descent method for solutions of equilibrium problems and other problems in fixed point theory

Abstract

Abstract In this paper, we combine the gradient projection algorithm and the hybrid steepest descent method and prove the strong convergence to a common element of the equilibrium problem; the null space of an inverse strongly monotone operator; the set of fixed points of a continuous pseudocontractive mapping and the minimizer of a convex function. This common element is proved to be the unique solution of a variational inequality problem. MSC:47H06, 47H09, 47J05, 47J25.