Holder continuity of solution maps to parametric set-valued Ky Fan inequalities

We first introduce notions of strong t-quasiconvexity and strong t-quasiconvex-likeness along with relaxed Holder continuity with respect to an ordering cone of a set-valued map. Then, these new conditions are utilized to establish sufficient conditions for the non-emptiness of solution sets and the stability in the sense of Holder continuity of solution maps to parametric set-valued Ky Fan inequalities. Our approach is different from the existing ones. At the end of the paper, we present an application of the main results to set-valued Nash equilibrium in games.

Automated summary

This paper introduces the concepts of strong t-quasiconvexity and strong t-quasiconvex-likeness, as well as relaxed Holder continuity, with respect to an ordering cone of a set-valued map. These concepts are then used to establish sufficient conditions for the non-emptiness of solution sets and the stability, in terms of Holder continuity, of solution maps to parametric set-valued Ky Fan inequalities. The approach presented in this paper is different from existing ones. Furthermore, an application of the main results to set-valued Nash equilibrium in games is also provided.