On the Generalized Implicit Quasivariational Inequalities

Generalized Strongly Nonlinear Implicit Quasivariational Inequalities

Generalized Nonlinear Implicit Quasivariational Inclusions

We introduce and study a new class of generalized nonlinear implicit quasivariational inclusions involving relaxed Lipschitzian mappings. We prove the existence of solution for the generalized nonlinear implicit quasivariational inclusions and construct some new stable perturbed iterative algorithms with errors. We also give an application to a class of generalized nonlinear implicit variationa...

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...

Existence for Competitive Equilibrium by Means of Generalized Quasivariational Inequalities

and Applied Analysis 3 3. Equilibrium Model We consider a marketplace consisting of two types of agents: n consumers, indexed by a, and m producers, indexed by b. We denote with A = {1, . . . , n}, B = {1, . . . , m}, and J = {1, . . . , l}, respectively, sets of consumers, producers, and goods. We denote by e a and x a the nonnegative quantities of commodity j, respectively, owned and consumed...

On the solution existence of implicit quasivariational inequalities with discontinuous multifunctions

In this paper we established some solution existence theorems for implicit quasivariational inequalities. We first established some results in finite-dimensional spaces and then a solution existence result in infinite-dimensional spaces was derived. Our theorems are proved for discontinuous mappings and sets which may be unbounded. The results presented in this paper are improvements of results...