We introduce new and interesting model of system of generalized set-valued equilibrium problems which generalizes and unifies the system of set-valued equilibrium problems, the system of generalized implicit vector variational inequalities, the system of generalized vector and vector-like variational inequalities introduced by Ansari et al. (2002), the system of generalized vector variational i...

In this paper, we consider different kinds of generalized invexity for vector valued functions and a vector optimization problem. Some relations between some vector variational-like inequalities and a vector optimization problem are established using the properties of Mordukhovich limiting subdifferentials under C − η−strong pseudomonotonicity. Mathematics Subject Classification (2010): 26A51, ...

In this paper, by introducing some new concepts in minimal spaces, we prove a generalized form of the Fan-KKM theorem vector spaces. A class F-implicit variational inequality problems and, as an application is investigated. Moreover, existence for kind under suitable assumptions spaces given.

Variational inequalities theory has been widely used in many fields, such as economics, physics, engineering, optimization and control, transportation [1, 4]. Like convexity to mathematical programming problem (MP), monotonicity plays an important role in solving variational inequality (VI). To investigate the variational inequality, many kinds of monotone mappings have been introduced in the l...

Mond-Weir type duals for multiobjective variational problems are formulated. Under generalized vector variational type I invexity assumptions on the functions involved, sufficient optimality conditions, weak and strong duality theorems are proved efficient and properly efficient solutions of the primal and dual problems.