Summary: We introduce an iterative algorithm for finding a common element of the set of solutions of a mixed equilibrium problem, the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of some variational inequality. Furthermore, we prove that the proposed iterative algorithm converges strongly to a common element of the above three sets. Our results extend and improve the corresponding results of L. C. Zeng
and J. C. Yao
[A hybrid iterative scheme for mixed equilibrium problems and fixed point problems, J. Comput. Appl. Math. 214, 186–201 (2008)], S. Takahashi
and W. Takahashi
[J. Math. Anal. Appl. 331, No. 1, 506–515 (2007; Zbl 1122.47056
)] and many others.