We introduce and study a new class of generalized nonlinear variational-like inequalities and prove an existence theorem of solutions for this kind of generalized nonlinear variational-like inequalities. By using the auxiliary principle technique, we construct a new iterative scheme for solving the class of the generalized nonlinear variational-like inequalities. The convergence of the sequence...

Various measures for the accuracy of approximate eigenstates of semibounded self-adjoint operators H in quantum theory, derived, e.g., by some variational technique, are scrutinized. In particular, the matrix elements of the commutator of the operatorH and (suitably chosen) different operators with respect to degenerate approximate eigenstates of H obtained by the variational methods are propos...

in this paper we propose a descent method for solving variational inequality problems where the underlying operator is nonsmooth, locally Lipschitz, and monotone over a closed, convex feasible set. The idea is to combine a descent method for variational inequality problems whose operators are nonsmooth, locally Lipschitz, and strongly monotone, with the Tikonov-Browder regularization technique....

This paper is devoted to the study of a new class of nonconvex variational inequalities, named general regularized nonconvex variational inequalities. By using the auxiliary principle technique, a new modified predictor–corrector iterative algorithm for solving general regularized nonconvex variational inequalities is suggested and analyzed. The convergence of the iterative algorithm is establi...

h this paper, we use the auxiliary principle technique to suggest a new &ass of predictor-corrector algorithms for solving generalized variational inequalities. The convergence of the proposed method only requires the partially relaxed strongly monotonicity of the operator, which is weaker than co-coercivity. As special cases, we obtain a number of known and new results for solving va,rious cla...

In this paper, we introduce and consider a class of variational inequalities, which is called the trifunction variational inequality. We use the auxiliary principle technique to suggest and analyze an implicit iterative methods for solving the trifunction variational inequalities. We study the convergence criteria of this new method under pseudomomotonicity condition, which is weaker condition ...

A new generalized nonlinear variational-like inequality is introduced and studied. By applying the auxiliary principle technique and KKM theory, we construct a new iterative algorithm for solving the generalized nonlinear variational-like inequality. By means of the Banach fixed-point theorem, we establish the existence and uniqueness of solution for the generalized nonlinear variational-like i...

In this paper, we consider extended general variational inequalities involving nonlinear operators. Using projection operator technique, we show that extended general variational inequality is equivalent to a fixed point problem. Using this alternative equivalent formulation, we propose and analyze some new algorithms for solving extended general variational inequalities and its variant forms. ...

In this paper, we introduce a new class of variational inequalities involving two operators. Using the projection technique, we establish the equivalence between the multivalued general variational inequalities and the fixed point problems. This equivalent formulation is used to suggest and analyze some iterative algorithms for solving the multivalued general variational inequalities. We also d...

We introduce and consider a new class of equilibrium problems and variational inequalities involving bifunction, which is called the nonconvex bifunction equilibrium variational inequality. We suggest and analyze some iterative methods for solving the nonconvex bifunction equilibrium variational inequalities using the auxiliary principle technique. We prove that the convergence of implicit meth...