Convex selections of multifunctions and their applications

Abstract

The notion of upper separated set-valued functions which forms a necessary and sufficient condition for the existence of convex selections for convex-valued multifunctions is introduced. The results obtained in this article lead to a new class of the multifunctions admitting continuous selections and therefore they are applicable to the existence of solutions to differential and stochastic inclusions.

†Dedicated to N.U. Ahmed on the occassion of his 70th birthday.

Keywords:

• Upper separated multifunction
• Legendre–Fenchel transform
• Differential and stochastic inclusion

Keywords:

• Mathematics Subject Classifications 2000: Primary: 47H04
• Secondary: 49J53
• 60H05

Notes

†Dedicated to N.U. Ahmed on the occassion of his 70th birthday.