A new iterative algorithm for equilibrium and fixed point problems of nonexpansive mapping

In this paper, a new iterative algorithm involving nonexpansive mapping in Hilbert space is proposed and proved to be strongly convergent to a point which is simultaneously a fixed point of a nonexpansive mapping and a solution of an equilibrium problem. The results of the paper extend previous results, see, for instance, Takahashi and Takahashi (2007), and other results in this field. Moreover, this algorithm is applied to find zeros of a maximal monotone operator and solve an optimization problem.