Journal of Convex Analysis 18 (2011), No. 4, 1047--1064
Copyright Heldermann Verlag 2011
Contingent Epiderivatives of Functions on Time Scales
Ewa Girejko
Faculty of Computer Science, Bialystok University of Technology, 15-351 Bialystok, Poland
e.girejko@pb.edu.pl
Dorota Mozyrska
Faculty of Computer Science, Bialystok University of Technology, 15-351 Bialystok, Poland
d.mozyrska@pb.edu.pl
Malgorzata Wyrwas
Faculty of Computer Science, Bialystok University of Technology, 15-351 Bialystok, Poland
m.wyrwas@pb.edu.pl
We characterize functions defined on times scales by the contingent epiderivative. Relations between delta and nabla derivatives and the contingent epiderivative of functions defined on time scales are investigated. We formulate two notions that are exploited in optimal control theory, namely the Fermat Rule and pseudo-convexity. Appropriate illustrative examples are presented.
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