A class of variational-hemivariational inequalities is studied in this paper. An inequality in the class involves two nonlinear operators and two nondifferentiable functionals, of which at least one is convex. An existence and uniqueness result is proved for a solution of the inequality. Continuous dependence of the solution on the data is shown. Convergence is established rigorously for finite...

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, minimax principles are explored for elliptic mixed hemivariational–variational inequalities. Under certain conditions, a saddle-point formulation is shown to be equivalent inequality. While the principle of independent interest, it employed in paper provide an elementary proof solution existence Theoretical results illustrated applications two contact problems.

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 paper, with the help of the duality operator and K. Fan’s lemma, we present existence results for strong vector equilibrium problems, under pseudomonotonicity assumptions and without any pseudomonotonicity assumptions, respectively. Then, as an application, the main results allow us to state existence theorems for strong vector variational inequality problems.