Split Systems of Nonconvex Variational Inequalities and Fixed Point Problems on Uniformly Prox-Regular Sets

Existence Theorems for Some Systems of Quasi–variational Inequalities Problems on Uniformly Prox–regular Sets

In this paper, some systems of quasi-variational inequality problems are considered on a class of nonconvex sets, as uniformly prox-regular sets. Some sufficient conditions for the existence solution of the considered problems are provided. Also, some interesting remarks are discussed. The results which are presented in this paper are more general, and may be viewed as an extension, improvement...

Regularization of differential variational inequalities with locally prox-regular sets

This paper studies, for a differential variational inequality involving a locally prox-regular set, a regularization process with a family of classical differential equations whose solutions converge to the solution of the differential variational inequality. The concept of local prox-regularity will be termed in a quantified way, as (r, α)-prox-regularity.

Nonlocal-interaction equations on uniformly prox-regular sets

We study the well-posedness of a class of nonlocal-interaction equations on general domains Ω⊂Rd , including nonconvex ones. We show that under mild assumptions on the regularity of domains (uniform prox-regularity), for λ -geodesically convex interaction and external potentials, the nonlocal-interaction equations have unique weak measure solutions. Moreover, we show quantitative estimates on t...

Viscosity Iterative Schemes for Finding Split Common Solutions of Variational Inequalities and Fixed Point Problems

and Applied Analysis 3 where S1 is a nonexpansive mapping. They proved that the sequence {xn} defined by 1.6 strongly converge to x∗ ∈ F S1 ⋂ VI C, T , if the coefficient αn, λn satisfy the following conditions:

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points