The analysis of the connections among generalized systems, Vector Optimization Problems and Variational Inequalities allows to deepen the study of the properties of the Minty Vector Variational Inequality. In particular, under suitable regularity assumptions,the equivalence between Minty Vector Variational Inequality and Stampacchia Vector Variational Inequality is shown.

This paper presents an iterative method for solving the generalized nonlinear set-valued mixed quasi-variational inequality, a problem class that was introduced by Huang, Bai, and Kang, [Comp. Math. Appl., 40, 2000]. The method incorporates step size controls that enable application to problems where certain set-valued mappings do not always map to nonempty closed bounded sets.

In this paper, we introduce a new kind of exceptional family for a class of mixed variational inequality problem (in short MVIPs) in a Hilbert space. Based on which and the topological degree theory, we obtain an alternative theorem and some existence theorems. Mathematics Subject Classification: 49J40; 47J20

A mixed variational formulation of the Brinkman problem is presented which is uniformly well–posed for degenerate (vanishing) coefficients under the hypothesis that a generalized Poincaré inequality holds. The construction of finite element schemes which inherit this property is then considered.

Convex and non-convex fuzzy mappings are well known to be important in the research of optimization. Symmetry idea convexity closely related. Therefore, concept symmetry is discussion inequalities because how its definition behaves. This study aims consider new class generalized variational-like inequality for mapping which as perturbed mixed inequality. We also introduce strongly variational i...

In this paper, we introduce and study a mixed variational inclusion problem involving infinite family of fuzzy mappings. An iterative algorithm is constructed for solving a mixed variational inclusion problem involving infinite family of fuzzy mappings and the convergence of iterative sequences generated by the proposed algorithm is proved. Some illustrative examples are also given.

‎in this paper we study the existence of nontrivial‎ solutions for a variational inequality on the half-line‎. ‎our‎ ‎approach is based on the non-smooth critical point theory‎ ‎for szulkin-type functionals.