Abstract
We first introduce notions of strong t-quasiconvexity and strong t-quasiconvex-likeness along with relaxed Hölder 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 Hölder 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.
Acknowledgments
The author would like to thank two anonymous referees for their valuable remarks and suggestions that helped significantly improve the paper.
Disclosure statement
No potential conflict of interest was reported by the author(s).