In this paper we consider an abstract class of time-dependent quasi variational–hemivariational inequalities which involves history-dependent operators and a set unilateral constraints. First, establish the existence uniqueness solution by using recent result for elliptic in reflexive Banach spaces combined with fixed-point principle operators. Then, apply to show unique weak solvability quasis...

Variational inequalities with linear inequality constraints are widely used in constrained optimization and engineering problems. By extending a new recurrent neural network [14], this paper presents a recurrent neural network for solving variational inequalities with general linear constraints in real time. The proposed neural network has onelayer projection structure and is amenable to parall...

In recent years, the variational inequality framework has been recognized as a powerful modelling tool in operations research and economics, whenever equilibrium relationships among several agents occur. This interest has prompted researchers to develop eecient algorithms for solving variational inequalities in nite dimensional spaces. In this presentation we will try to assess the advantages a...

A mathematical model which describes an explicit time-dependent quasistatic frictional contact problem between a deformable body and a foundation is introduced and studied, in which the contact is bilateral, the friction is modeled with Tresca’s friction law with the friction bound depending on the total slip, and the behavior of the material is described with a viscoelastic constitutive law wi...

We prove a strong convergence result for a sequence generated by Halpern's type iteration for approximating a common fixed point of a countable family of quasi-Lipschitzian mappings in a real Hilbert space. Consequently, we apply our results to the problem of finding a common fixed point of asymptotically nonexpansive mappings, an equilibrium problem, and a variational inequality problem for co...

In this paper we consider a class of feedback control systems described by an evolution hemivariational inequality involving history-dependent operators. Under the mild conditions, first, prove priori estimates solutions to system. Then, existence theorem for system is obtained using well-known Bohnenblust-Karlin fixed point theorem. Moreover, optimal problem driven system, and establish its so...

Background Equilibrium is a central concept in numerous disciplines including economics, management science/operations research, and engineering. Methodologies that have been applied to the formulation , qualitative analysis, and computation of equilibria have included • systems of equations, • optimization theory, • complementarity theory, and • fixed point theory. Variational inequality theor...

In this short paper, we establish a variational expression of the Tsallis relative entropy. In addition, we derive a generalized thermodynamic inequality and a generalized Peierls-Bogoliubov inequality. Finally we give a generalized Golden-Thompson inequality.

We present some error bound results of generalized D-gap functions for nonsmooth and nonmonotone variational inequality (VI) problems. Application is given in providing a derivative-free descent method.

In this work, it is presented iterative schemes for achieving to common points of the solutions set of the system of generalized mixed equilibrium problems, solutions set of the variational inequality for an inverse-strongly monotone operator, common fixed points set of two infinite sequences of relatively nonexpansive mappings and common zero points set of two finite sequences of maximal monot...