A new hybrid iterative method for solution of equilibrium problems and fixed point problemsfor an inverse strongly monotone operatorand a nonexpansive mapping

摘要

In this paper, we introduce an iterative scheme by a new hybrid methodfor finding a common element of the set of fixed points of a nonexpansive map-ping, the set of solutions of an equilibrium problem and the set of solutions of thevariational inequality for a-inverse-strongly monotone mappings in a real Hilbertspace. We show that the iterative sequence converges strongly to a common elementof the above three sets under some parametric controlling conditions by the ewhybrid method which is introduced by Takahashi et al. (J. Math. Anal. Appl., doi:10.1016/j.jmaa.2007.09.062, 2007). The results are connected with Tada and Taka-hashi's result [A. Tada and W. Takahashi, Weak and strong convergence theorems fora nonexpansive mappings and an equilibrium problem, J. Optim. Theory Appl. 133,359-370, 2007]. Moreover, our esult is applicable to a wide class of mappings.