A new iterative method for equilibrium problems and fixed point problems (Q2016692)

Summary: Introducing a new iterative method, we study the existence of a common element of the set of solutions of equilibrium problems for a family of monotone, Lipschitz-type continuous mappings and the sets of fixed points of two nonexpansive semigroups in a real Hilbert space. We establish strong convergence theorems of the new iterative method for the solution of the variational inequality problem which is the optimality condition for the minimization problem. Our results improve and generalize the corresponding recent results of \textit{P. N. Anh} [J. Optim. Theory Appl. 154, No. 1, 303--320 (2012; Zbl 1270.90100)], \textit{F. Cianciaruso} et al. [J. Optim. Theory Appl. 146, No. 2, 491--509 (2010; Zbl 1210.47080)], and many others.