In this paper, we introduce a new class of bifunction variational inequalities, which is called the multivalued mixed quasi bifunction variational inequalities. Using the auxiliary principle technique, we suggest and analyze a proximal point method for solving the multivalued mixed quasi bifunction variational inequalities. It is shown that the convergence of the proposed method requires only p...

In this paper, a novel modified proximal dynamical system is proposed to compute the solution of mixed variational inequality problem (MVIP) within fixed time, where time convergence finite and uniformly bounded for all initial conditions. Under assumptions strong monotonicity Lipschitz continuity, it shown that exists, uniquely determined, converges unique associated MVIP time. Furthermore, fi...

In this paper, an equivalent minimization principle is established for a hemivariational inequality of the stationary Stokes equations with nonlinear slip boundary condition. Under certain assumptions on data, it shown that there unique minimizer problem, and furthermore, mixed formulation has solution. The proof result based basic knowledge convex minimization. For comparison, in existing lite...

Pseudomonotone∗ maps are a generalization of paramonotone maps which is very closely related to the cutting plane property in variational inequality problems (VIP). In this paper, we first generalize the so-called minimum principle sufficiency and the maximum principle sufficiency for VIP with multivalued maps. Then we show that pseudomonotonicity∗ of the map implies the “maximum principle suff...

The purpose of this work to investigate pseudomonotone and Lipschitz continuous variational inequalities in real Hilbert spaces. For solving problem, we propose two new methods which combine advantages the subgradient extragradient method projection contraction method. Similar some recent developments, proposed do not require knowledge constant associated with inequality mapping. Under suitable...

given a mapping $f:xto x$ we naturally associate to it a monotonic map $gg_f:exp xto exp x$ from the power set of $x$ into itself, thus inducing a generalized topology on $x$. in this paper we investigate some properties of generalized topologies which are defined by such a procedure.

Abstract This paper introduces a triple-adaptive subgradient extragradient process with extrapolation to solve bilevel split pseudomonotone variational inequality problem (BSPVIP) the common fixed point constraint of finitely many nonexpansive mappings. The under consideration is in real Hilbert spaces, where BSPVIP involves demimetric mapping. proposed rule exploits strong monotonicity one ope...

For the quasi-equilibrium problem where the players' costs and their strategies both depend on the rival's decisions, an alternative extragradient projection method for solving it is designed. Different from the classical extragradient projection method whose generated sequence has the contraction property with respect to the solution set, the newly designed method possesses an expansion proper...

In this paper, an alternative approach is provided in the well-posedness analysis of elliptic variational–hemivariational inequalities real Hilbert spaces. This includes unique solvability and continuous dependence solution on data. most existing literature inequalities, results are obtained by using arguments surjectivity for pseudomonotone multivalued operators, combined with additional compa...