广义平衡与不动点问题的黏性逼近

Viscosity Approximation Method for Generallized Equilibrium Problems and Fixed Point Problems

本文的目的是在Hilbert空间中引入和研究了一种新的迭代序列,用以寻求具逆一强单调映象的广义平衡问题的解集与无限簇非扩张映象的不动点集的公共元.在适当的条件下,用黏性逼近法证明了逼近于这一公共元的强收敛定理.应用该结论,我们证明了逼近于平衡问题和变分不等式问题的强收敛定理.所得结果改进和推广了文献的相应结果.

The purpose of this paper is to introduce a new iterative scheme for finding a common element of the set of solutions of a generalized equilibrium problem with inverse-strongly monotone mapping and the set of common fixed point for a family of infinite nonexpansive mappings in Hilbert space.It is shown that under suitable conditions by the viscosity approximation methods,some strong convergence theorems for approximating to this common elements are proved.Using this result,we prove two new strong convergence theorems in equilibrium problems and variational inequalities.The results presented in the paper extend and improve some recent results.