Approximation algorithm for fixed points of nonlinear operators and solutions of mixed equilibrium problems and variational inclusion problems with applications

The purpose of this paper is to introduce an iterative algorithm for finding a common element of the set of fixed point of nonexpansive mappings, set of a mixed equilibrium problem and the set of variational inclusions in a real Hilbert space. We prove that the sequence x(n) which is generated by the proposed iterative algorithm converges strongly to a common element of four sets above. Furthermore, we give an application to optimization and some numerical examples which support our main theorem in the last part. Our result extended and improve the existing result of Yao et al. [19] and references therein.