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Abstract: 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. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce an iterative method to approximate a common solution of a split equilibrium problem, a variational inequality problem and a fixed point problem for a nonexpansive mapping in real Hilbert spaces. We prove that the sequences generated by the iterative scheme converge strongly to a common solution of the split equilibrium problem, the variational inequality problem and the fixed point problem for a nonexpansive mapping. The results presented in this paper extend and generalize many previously known results in this research area. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a system of nonlinear variational-like inclusions (SNVLI) in Hilbert spaces. In particular, SNVLI reduces to a variational inclusion, an extension of variational inclusion studied by Hassouni and Moudafi [1]. Using fixed-point method, we suggest an iterative algorithm for finding an approximate solution to SNVLI. Further, we prove the existence of solution and discuss convergence criteria for the approximate solution of SNVLI. The theorems presented in this paper improve and unify many known results of variational inclusions and variational inequalities, see for example [1–3]. [Copyright &y& Elsevier]