In this paper, we introduce and consider a new class of equilibrium variational inequalities, called the mixed general equilibrium bifunction variational inequalities. We suggest and analyze some proximalmethods for solvingmixed general equilibriumbifunction variational inequalities using the auxiliary principle technique. Convergence of these methods is considered under somemild suitable condi...

The purpose of this paper is to introduce and study a new class of generalized vector variational-like inequalities and generalized vector variational inequalities in fuzzy environment. By using the KKM-technique, Maximal Element Lemma and under suitable conditions, some existence theorems of solutions for these two kinds of vector variational inequalities in fuzzy environment are proved. The r...

n this paper, we introduce and consider a new class of equilibrium problems and variational inequalities which is called the nonconvex equilibrium variational inequality. We suggest and analyze some iterative methods for solving the nonconvex equilibrium variational inequalities using the auxiliary principle technique. We prove that the convergence of implicit method requires only monotonicity....

In this paper, we consider a new system of quasi variational inequalities involving two different operators. Using the projection technique, we suggest and analyze a new iterative method for solving this system of quasi variational inequalities. We also prove the convergence of this iterative method under some mild conditions. As a special case, our results include the results of Huang and Noor...

In this paper, we propose the new concept of optimal solution for fuzzy variational problems based on the possibility and necessity measures. Inspired by the well–known embedding theorem, we can transform the fuzzy variational problem into a bi–objective variational problem. Then the optimal solutions of fuzzy variational problem can be obtained by solving its corresponding biobjective variatio...

Fractional calculus has been used to model the physical and engineering processes that have found to be best described by fractional differential equations. For that reason, we need a reliable and efficient technique for the solution of fractional differential equations. The aim of this paper is to present an analytical approximation solution for linear and nonlinear multi-order fractional diff...

AbstractAn analytic technique, combination of two methods Homotopy Perturbation Method and Variational Iteration Method are applied for solve second kind of linear Volteera equations. homotopy perturbation method and variational iteration method are employed to solve Volteera integral equations. The result reveals that the homotopy perturbation method and variational iteration method are very e...

We introduce and study a class of generalized strongly nonlinear mixed variational-like inequalities, which includes several classes of variational inequalities and variational-like inequalities as special cases. By applying the auxiliary principle technique and KKM theory, we suggest an iterative algorithm for solving the generalized strongly nonlinear mixed variationallike inequality. The exi...

We use the technique of updating the solution to suggest and analyze a class of new splitting methods for solving general mixed variational inequalities. It is shown that these modified methods converge for pseudomonotone operators, which is a weaker condition than monotonicity. Our methods differ from the known threestep forward-backward splitting of Glowinski, Le Tallec, and M. A. Noor for so...

We implement a relatively new analytical technique, the variational iteration decomposition method (VIDM), for solving the eighth-order boundary value problems. The proposed method is an elegant combination of variational iteration method and decomposition method. The analytical results of the equations have been obtained in terms of convergent series with easily computable components. Numerica...