In this paper, a general system of variational inclusions in Banach Spaces is introduced. An iterative method for finding solutions of a general system of variational inclusions with inverse-strongly accretive mappings and common set of fixed points for a λ-strict pseudocontraction is established. Under certain conditions, by forward-backward splitting method, we prove strong convergence theore...

In recent years, sequential optimality conditions are frequently used for convergence of iterative methods to solve nonlinear constrained optimization problems. The sequential optimality conditions do not require any of the constraint qualications. In this paper, We present the necessary sequential complementary approximate Karush Kuhn Tucker (CAKKT) condition for a point to be a solution of a ...

We present solutions to the Eshelby conjectures based on a variational inequality. We first discuss the meanings of the original Eshelby’s statement. By Fourier analysis, we establish the connection between the homogeneous Eshelby inclusion problem and the classic Newtonian potential problem. We then proceed to the solutions of the Eshelby conjectures. Under some hypothesis on the material prop...

we introduce variational inequality problems on hilbert $c^*$-modules and we prove several existence results for variational inequalities defined on closed convex sets. then relation between variational inequalities, $c^*$-valued metric projection and fixed point theory  on  hilbert $c^*$-modules is studied.

We first prove that the product of a family of LΓ-spaces is also an LΓ-space. Then, by using a Himmelberg type fixed point theorem in LΓ-spaces, we establish existence theorems of solutions for systems of generalized quasivariational inclusion problems, systems of variational equations, and systems of generalized quasiequilibrium problems in LΓ-spaces. Applications of the existence theorem of s...

We introduce several new kinds of inferior and superior limits and corresponding kinds of semicontinuity of a set-valued map. Together with the known concepts of semicontinuity, they can be used to have a clearer insight of local behaviors of maps. Then we investigate all major semicontinuity properties of solution maps to a general quasivariational inclusion. Consequences are derived for sever...

The main purpose of this paper consists of providing characterizations of the inclusion of the solution set of a given conic system posed in a real locally convex topological space into a variety of subsets of the same space de…ned by means of vector-valued functions. These Farkas-type results are used to derive characterizations of the weak solutions of vector optimization problems (including ...

We introduce and study a class of a system of random set-valued variational inclusion problems. Some conditions for the existence of solutions of such problems are provided, when the operators are contained in the classes of generalized monotone operators, so-called A,m, η -monotone operator. Further, the stability of the iterative algorithm for finding a solution of the considered problem is a...

We proposed in this paper a new iterative scheme for finding common elements of the set of fixed points of a finite family of quasi-nonexpansive mappings, the set of solutions of variational inclusion, and the set of solutions of generalized equilibrium problems. Some strong convergence results were derived by using the concept ofW-mappings for a finite family of quasi-nonexpansive mappings. St...