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

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.

Keywords:

• Ky Fan inequality
• Hölder continuity
• strong quasiconvexity
• strong quasiconvex-likeness
• set-valued Nash equilibrium

AMS CLASSIFICATIONs:

• 49K40
• 90C31
• 91B50

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).

Additional information

Funding

This is a result of the project [grant number B2022-TCT-02] supported by the Ministry of Education and Training of Viet Nam.