Strong convergence theorems for solving generalized mixed equilibrium problems and general system of variational inequalities by the hybrid method

In this paper, we introduce modified Mann iterative algorithms by the new hybrid projection method for finding a common element of the set of fixed points of a countable family of nonexpansive mappings, the set of solutions of the generalized mixed equilibrium problems and the set of solutions of the general system of the variational inequality for two inverse-strongly monotone mappings in a real Hilbert space. Strong convergence theorems of these processes are established which connected with minimize problems. Moreover, we also apply our main results to the W -mapping and the class of strictly pseudocontractive mappings. The results are improved and connected with Kumam’s result (2009, 2008) [28,29], Shinzato and Takahashi’s result (2001) [30], Tada and Takahashi’s result (2007) [14], Takahashi et al.’s result (2008) [31], and Plubtieng and Thammathiwat’s result [32], and some known corresponding results in the literatures.