The generalized contingent epiderivative of set-valued maps is introduced in this paper and its relationship to the contingent epiderivative is investigated. A unified necessary and sufficient optimality condition is derived in terms of the generalized contingent epiderivative. The existence of...

In this paper, we introduce the concept of approximate solutions for set-valued mappings and provide a sufficient condition for the existence of approximate solutions of set-valued mappings. We obtain an approximate variational principle for set-valued mappings. Copyright Springer-Verlag Berlin...

We define a notion of measure of discontinuity and establish an existence theorem of approximate fixed point for discontinuous set-valued maps, generalizing the fixed point theorem of Kakutani. Copyright Springer-Verlag Berlin Heidelberg 1998

In this paper we introduce the concept of the contingent epiderivative for a set-valued map which modifies a notion introduced by Aubin [2] as upper contingent derivative. It is shown that this kind of a derivative has important properties and is one possible generalization of directional...

Two types of rod antennas of mobile phones are optimized so that the radiated energy absorbed by the head or body of the user is reduced and the radiation intensity to other areas especially to the receiver is increased. The mathematical modelling of this problem leads to an infinite dimensional...