A Nonlinear Scalarization Function and Generalized Quasi-vector Equilibrium Problems

Semicontinuity of the Solution Mapping to a Parametric Generalized Weak Ky Fan Inequality

“…Proposition 4 (see [24]). The function defined in Definition 3 satisfies the following propositions:…”

“…Definition 3 (see [24]). Let : × × → be a vectorvalued mapping and, for any ( , , ) ∈ × × , ( , , ) ∈ int ( , , ).…”

“…In this paper, we are interested in the study of the semicontinuity of the solution mapping to a class of parametric generalized weak Ky Fan inequality with moving cones. To avoid using the assumptions involving the information about the solution set, we establish some new assumptions and obtain the upper and lower semicontinuity of the solution mapping to the parametric generalized weak Ky Fan inequality by using a nonlinear scalarization function defined in [24], which is different from the nonlinear scalarization functions defined in [20,21].…”

On the Relationship Between Topological Boundedness and the Ordered Boundedness for Solid Cones via Scalarizing

“…The next definition was firstly introduced in [5] (for more details, see [6]) in order to apply in optimization theory and then was used for equilibrium problems in [1]. Definition 1.9.…”

The Hölder continuity of solutions to generalized vector equilibrium problems

“…Many authors (see [8,9,12,17,18]) have intensively studied different types of vector equilibrium problems. The stability analysis of solution maps for equilibrium problems is an important topic in optimization theory and applications.…”