Strongly nonlinear quasivariational inequalities

Generalized Strongly Nonlinear Implicit Quasivariational Inequalities

On the Generalized Strongly Nonlinear Implicit Quasivariational Inequalities for Set-valued Mappings

In this paper, we introduce and study a new class of generalized strongly nonlinear implicit quasivariational inequalities for set-valued mappings and construct some new iterative algorithms for these kinds of generalized strongly nonlinear implicit quasivariational inequalities by using the projection method and Nadler’s theorem. We prove some existence theorems of solutions for these kinds of...

Parametric generalized strongly nonlinear mixed quasivariational inclusions in Banach spaces

In this paper, by using the concept of the resolvent operator, we study the behavior and sensitivity analysis of the solution set for a class of parametric generalized strongly nonlinear mixed quasivariational inclusion problem in Banach spaces. The results presented in this paper are new and generalize many known results in this field. Mathematics Subject Classification: 49J40, 90C20

On Uniqueness in Evolution Quasivariational Inequalities

We consider a rate independent evolution quasivariational inequality in a Hilbert space X with closed convex constraints having nonempty interior. We prove that there exists a unique solution which is Lipschitz dependent on the data, if the dependence of the Minkowski functional on the solution is Lipschitzian with a small constant and if also the gradient of the square of the Minkowski functio...

Extended Well-posedness for Quasivariational Inequalities

In this paper, we introduce the concepts of extended well-posedness for quasivariational inequalities and establish some characterizations. We show that the extended well-posedness is equivalent to the existence and uniqueness of solutions under suitable conditions. In addition, the corresponding concepts of extended well-posedness in the generalized sense are introduced and investigated for qu...