广义黏性隐迭代序列的均衡问题和不动点问题

Equilibrium Problems and Fixed Point Problems of the Generalized Viscosity Implicit Iteration

利用黏性逼近方法构造了一种新的非扩张映射广义隐迭代序列,在Hilbert空间研究了此序列的均衡问题与不动点问题,并在适当条件下证明了此序列强收敛于非扩张映射的不动点集和均衡问题解集的公共元。

In this paper, we introduce a generalized implicit scheme using the viscosity approximation technique, and study equilibrium problems and fixed point problems of nonexpansive mappings in Hilbert spaces. We prove that the suggested method converges strongly to a special common element of the solutions of equilibrium problems and the set of fixed points of nonexpansive mappings under some conditions.