In this paper, we introduce a new class of general mixed vector F -implicit complementarity problems and general mixed vector F -implicit variational inequality problems, and study the equivalence between of them under certain assumptions in Banach spaces. We also derive some new existence theorems of solutions for the general mixed vector F -implicit complementarity problems and the general mi...

In this paper, we introduce and study a new class of generalized mixed quasi-variational-like inequalities. Using the auxiliary principle technique, we construct a new iterative algorithm for finding the approximate solutions of the generalized mixed quasi-variational-like inequality. An existence result of solutions for the generalized mixed quasi-variational-like inequality and the convergenc...

In this paper, the concept of well-posedness for a minimization problem is extended to develop the concept of well-posedness for a class of strongly mixed variationalhemivariational inequalities with perturbations which includes as a special case the class of variational-hemivariational inequalities with perturbations. We establish some metric characterizations for the well-posed strongly mixed...

We use the auxiliary principle technique to suggest and analyze some iterative methods for solving a new class of variational inequalities, which is called the mixed trifunction variational inequality. The mixed trifunction variational inequality includes the trifunction variational inequalities and the classical variational inequalities as special cases. Convergence of these iterative methods ...

In this paper, we consider mixed vector variational-like inequality problems in the setting of topological vector spaces. We extend the concept of upper sign continuity for vector-valued mappings. Further, by exploiting KKM-Fan lemma, we establish some existence results for solutions of mixed vector variational-like inequality problems and show that the solution sets of these problems are compact.

We introduce and study a new class of generalized nonlinear mixed variational-like inequalities in reflexive Banach spaces. By applying Ding’s technique we prove several existence and uniqueness theorems of solutions for the generalized nonlinear mixed variational-like inequality, extend the auxiliary problem technique to suggest and analyze an iterative method to compute the approximate soluti...

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 ...

In this work, it is presented iterative schemes for achieving to common points of the solutions set of the system of generalized mixed equilibrium problems, solutions set of the variational inequality for an inverse-strongly monotone operator, common fixed points set of two infinite sequences of relatively nonexpansive mappings and common zero points set of two finite sequences of maximal monot...

We introduce a new hybrid iterative algorithm for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings, the set of solutions of the variational inequality of a monotone mapping, and the set of solutions of a mixed equilibrium problem. This study, proves a strong convergence theorem by the proposed hybrid iterative algorithm which solves fixed-point ...

We consider an extension of the notion of well-posedness by perturbations, introduced by Zolezzi 1995, 1996 for a minimization problem, to a class of generalized mixed variational inequalities in Banach spaces, which includes as a special case the class of mixed variational inequalities. We establish some metric characterizations of the well-posedness by perturbations. On the other hand, it is ...