均衡问题和不动点问题的粘滞近似方法及其应用

Viscosity Approximation Methods for Equilibrium Problems and Fixed Point Problems with Its Applications

用粘滞近似方法产生了一个新的迭代序列,并证明了该迭代序列强收敛于一个非扩张映射的不动点,同时该不动点也是一个变分不等式和一个均衡问题的共同解.作为应用,另外证明了一个关于非扩张映射和严格伪压缩映射的定理.

We introduce a new iterative scheme by viscosity approximation method for obtaining a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping and an inverse-strongly monotone mapping in a Hilbert space. Then a strong convergence theorem is obtained. As its application, we give a strong convergence theorem for nonexpansive mappings and strictly pseudo-contractive mappings in a Hitbert space.