The hybrid steepest descent method for solutions of equilibrium problems and other problems in fixed point theory
M.O. Osilike, Eric U. Ofoedu, Felix U Attah · Fixed Point Theory and Applications · 2014
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.