Abstract
In this paper, we prove that, for every vector quasi-equilibrium problem, there exists at least one essential component of the set of its solutions. As application, we show that, for every system of vector quasi-equilibrium problems, there exists at least one essential component of the set of its solutions in the uniform topological space of objective functions and constraint mappings.
Highlights
Essential component has been an important aspect in the study of stability for nonlinear problems
Lin [ ] established essential components of the solution set for SGVQEP under perturbations of the best-reply map
No paper has established essential components of the solution set for SVQEP, SGVQEP or SGVQEPS under perturbations of objective functions and constraint mappings
Summary
Essential component has been an important aspect in the study of stability for nonlinear problems. Lee, Yang [ ] studied the system of generalized vector quasi-equilibrium problems with set-valued maps (briefly, SGVOEPS). Yi be real Hausdorff topological vector spaces and Ki a nonempty subset of Xi. For each i ∈ I, let Ci be a closed, convex and pointed cone of Yi with int Ci = ∅, where int Ci denotes the interior of Ci. Let K =
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