DEMICONTINUITY, GENERALIZED CONVEXITY AND LOOSE SADDLE POINTS OF SET-VALUED MAPS

Abstract

The aim of this paper is to establish the existence of loose saddle points for a set-valued map which is defined in a topological vector space and possesses the demicontinuity and generalized convexity. Our results strengthen several previously obtained results on the existence of saddle and loose saddle points for single- or set-valued maps.

Keywords:

• Demicontinuity
• Generalized convexity
• Loose saddle point
• Saddle point
• Set-valued map