Strong convergence theorem for the modified generalized equilibrium problem and fixed point problem of strictly pseudo-contractive mappings

The purpose of this paper is to modify the generalized equilibrium problem introduced by Ceng et al. (J. Glob. Optim. 43:487-502, 2012) and to introduce the K-mapping generated by a finite family of strictly pseudo-contractive mappings and finite real numbers modifying the results of Kangtunyakarn and Suantai (Nonlinear Anal. 71:4448-4460, 2009). Then we prove the strong convergence theorem for finding a common element of the set of fixed points of a finite family of strictly pseudo-contractive mappings and a finite family of the set of solutions of the modified generalized equilibrium problem. Moreover, using our main result, we obtain the additional results related to the generalized equilibrium problem.