Extended General Nonlinear Quasi-Variational Inequalities and Projection Dynamical Systems

Graph convergence with an application for system of variational inclusions and fixed-point problems

“…During the last six decades, variational inequality theory, originally introduced for the study of partial differential equations by Hartman and Stampacchia [1], has been recognized as a strong tool in the mathematical study of many nonlinear problems of physics and mechanics, as the complexity of the boundary conditions and the diversity of the constitutive equations lead to variational formulations of inequality type. As many nonlinear problems arising in optimization, operations research, structural analysis, and engineering sciences can be transformed into variational inequality problems (see, e.g., [2,3]), since the appearance of this theory, there has been an increasing interest in extending and generalizing variational inequalities in many different directions using novel and innovative techniques, see, for example, [4,5] and the references therein. Without doubt, one of the most important and well-known generalizations of variational inequalities is variational inclusions and thanks to their wide applications in the optimization and control, economics and transportation equilibrium, engineering science, etc., the study of different classes of variational inclusion problems continues to attract the interest of many researchers.…”

“…The existence of a strong connection between the variational inequality problems and the fixed-point problems motivated many investigators to study the problem of finding common elements of the set of solutions of variational inequalities/inclusions and the set of fixed points of given operators. For more details and information, the reader is referred to [4,[38][39][40][41][42][43][44][45][46] and the references therein.…”

A modified inertial projection and contraction algorithms for quasi-variational inequalities

“…We denote by SOL(C, F) the solution set of (1.2) in this paper. For solving the QVI and the VI, many results were obtained via iteration methods in infinite dimensional spaces; see, e.g., [2,3,9,16,18,23] and the references therein. An efficient method, known as the gradient-projected method, is as follows…”

Dynamical systems for quasi variational inequalities

“…We remark that if the involved set does not depend upon the solution then quasi variational inequality reduces to the variational inequality, the origin of which can be traced back to Stampacchia [27]. Variational inequalities and quasi variational inequalities provide us a unifying and an efficient framework to study various related and unrelated problems which arise in different branches of pure and applied sciences; see [1,2,8,11,12,16,19,20,23,24,25,28] and references therein.…”