a concept of weak $f$-property for a set-valued mapping is introduced‎, ‎and then under some suitable assumptions‎, ‎which do not involve any information‎ ‎about the solution set‎, ‎the lower semicontinuity of the solution mapping to‎ ‎the parametric‎ ‎set-valued vector equilibrium-like problems are derived by using a density result and scalarization method‎, ‎where the‎ ‎constraint set $k$...

A concept of weak $f$-property for a set-valued mapping is introduced‎, ‎and then under some suitable assumptions‎, ‎which do not involve any information‎ ‎about the solution set‎, ‎the lower semicontinuity of the solution mapping to‎ ‎the parametric‎ ‎set-valued vector equilibrium-like problems are derived by using a density result and scalarization method‎, ‎where the‎ ‎constraint set $K$...

In this paper, by using a new concept of strong convexity, we obtain sufficient conditions for Holder continuity of the solution mapping for a parametric weak vector equilibrium problem in the case where the solution mapping is a general set-valued one. Without strong monotonicity assumptions, the Holder continuity for solution maps to parametric weak vector optimization problems is discussed.

In this paper, first a short history of the notion of equilibrium problem in Economics and Nash$acute{'}$ game theory is stated. Also the relationship between equilibrium problem among important mathematical problems like optimization problem, nonlinear programming, variational inequality problem, fixed point problem and complementarity problem is given. The concept of generalized pseudomonoton...

Traffic network equilibrium problems with capacity constraints of arcs are studied. A weak vector equilibrium principle with vector-valued cost functions, which are different from the ones in the work of Lin 2010 , and three kinds of parametric equilibrium flows are introduced. Some necessary and sufficient conditions for a weak vector equilibrium flow to be a parametric equilibrium flow are de...

In this paper, the lower semicontinuity and continuity of the solution mapping to a parametric generalized vector equilibrium problem involving set-valued mappings are established by using a new proof method which is different from the ones used in the literature.

This paper is devoted to the characterizations of the boundedness and nonemptiness of solution sets for set-valued vector equilibrium problems in reflexive Banach spaces, when both themapping and the constraint set are perturbed by different parameters. By using the properties of recession cones, several equivalent characterizations are given for the set-valued vector equilibrium problems to ha...

This paper deals with the characterization of solutions for vector equilibrium problems by means of conjugate duality. By using the Fenchel duality we establish variational principles, that is, optimization problems with set-valued objective functions, the solution sets of which contain the ones of the vector equilibrium problems. The set-valued objective mappings depend on the data, but not on...