STRONG CONVERGENCE THEOREMS FOR EQUILIBRIUM PROBLEMS, FIXED POINT PROBLEMS OF QUASI-NONEXPANSIVE MAPPINGS AND VARIATIONAL INEQUALITY PROBLEMS
Meng Li, Qiumei Sun, Haiyun Zhou · Journal of applied mathematics & informatics · 2013
In this paper, a new iterative algorithm involving quasi-nonexpansive mapping in Hilbert space is proposed and proved to be strongly convergent to a point which is simultaneously a fixed point of a quasi-nonexpansive mapping, a solution of an equilibrium problem and the set of solutions of a variational inequality problem. The results of the paper extend previous results, see, for instance, Takahashi and Takahashi (J Math Anal Appl 331:506-515, 2007), P.E.Maing $\acute{e}$ (Computers and Mathematics with Applications, 59: 74-79,2010) and other results in this field.