Quadratic minimization for equilibrium problem variational inclusion and fixed point problem

Abstract

借助预解式技巧,寻求二次极小化问题minx∈Ω‖x‖2的解,其中Ω是Hilbert空间中某一广义平衡问题的解集,与一无穷族非扩张映像的公共不动点的集合,以及某一变分包含的解集的交集.在适当的条件下,逼近上述极小化问题的解的一新的强收敛定理被证明. The purpose was by using the resolvent approach to find the solutions to the quadratic minimization problem:minx∈Ω‖x‖2,where Ω was the intersection set of the set of solutions to some generalized equilibrium problem,the set of common fixed points for an infinite family of nonexpansive mappings and the set of solutions to some variational inclusions in the setting of Hilbert spaces.Under suitable conditions some new strong convergence theorems for approximating to a solution of the above minimization problem were proved.