Some New Classes of General Harmonic-like Variational Inequalities
Abstract
Several new classes of general harmonic-like variational inequalities involving two arbitrary operators are introduced and considered in this paper. Some important cases are discussed, which can be obtained by choosing suitable and appropriate choice of the operators. Projection technique is applied to establish the equivalence between the general harmonic-like variational inequalities and fixed point problems. This alternative formulation is used to discuss the uniqueness of the solution as well as to propose a wide class of proximal point algorithms. Convergence criteria of the proposed methods is considered. Asymptotic stability of the solution is studied using the first order dynamical system associated with variational inequalities. Second order dynamical systems associated with general quasi variational inequalities are applied to suggest some inertial type methods. Some special cases are discussed as applications of the main results. We also show that the change of variable can be used to show that the harmonic-like variational inequalities. Several open problems are indicated for future research work.
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