Iterative algorithms for generalized mixed equilibrium problems

In this paper, we consider a generalized mixed equilibrium problem in real Hilbert space. Using the auxiliary principle, we define a class of resolvent mappings. Further, using fixed point and resolvent methods, we give some iterative algorithms for solving generalized mixed equilibrium problem. Furthermore, we prove that the sequences generated by iterative algorithms converge weakly to the solution of generalized mixed equilibrium problem. These results require monotonicity (θ-pseudo monotonicity) and continuity (Lipschitz continuity) for mappings.