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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 give a hybrid extragradient iterative method for finding the approximate element of the common set of solutions of a generalized equilibrium problem, a system of variational inequality problems, a variational inequality problem and a fixed point problem for a strictly pseudocontractive mapping in a real Hilbert space. Further we establish a strong convergence theorem based on this method. The results presented in this paper improves and generalizes the results given in Yao et al. and Ceng et al. , and some known corresponding results in the literature. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a generalized mixed equilibrium problem involving non-monotone set-valued mappings in real Hilbert space. We extend the notions of the Yosida approximation and its corresponding regularized operator given by Moudafi and Thera [A. Moudafi, M. Thera, Proximal and dynamical approaches to equilibrium problems, in: Lecture Notes in Econom. and Math. System, vol. 477, Springer-Verlag, Berlin, 2002, pp. 187–201] and discuss some of their properties. Further, we consider a generalized Wiener–Hopf equation problem and show its equivalence with the generalized mixed equilibrium problem. Using a fixed point formulation of the generalized Wiener–Hopf equation problem, we construct an iterative algorithm. Furthermore, we extend the notion of stability given by Harder and Hick [A.M. Harder, T.L. Hicks, Stability results for fixed-point iteration procedures, Math. Japonica 33 (5) (1998) 693–706]. We prove the existence of a solution and discuss the convergence and stability of the iterative algorithm for the generalized Wiener–Hopf equation problem. Since the generalized mixed equilibrium problems include variational inequalities as special cases, the results presented in this paper continue to hold for these problems. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a system of generalized variational-like inequality problems (SGVLIP) involving nondifferentiable terms, and its related auxiliary problems in real Hilbert spaces. An existence theorem for auxiliary problems is established. Further, by exploiting this theorem, an algorithm for the SGVLIP is constructed. Furthermore, we prove the existence of a unique solution of SGVLIP and discuss the convergence analysis of the algorithm. The technique and results presented in this paper generalize and unify the corresponding techniques and results given in [M.A. Noor, General nonlinear variational inequalities, J. Math. Anal. Appl. 126 (1987) 78–84; M.A. Noor, General variational inequalities, Appl. Math. Lett. 1 (1988) 119–122; M.A. Noor, Mixed variational-like inequalities, Commun. Appl. Nonlinear Anal. 1 (4) (1994) 63–75]. [Copyright &y& Elsevier]