"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science

Nonlinear multivalued analysis
Code
Semes-
ter
Hours: C+S+L
Credits
Type
Section
ME021
8
2+2+0
8
optional
Matematica Economica
ME021
8
2+2+0
8
optional
Matematici Aplicate
Teaching Staff in Charge
Assoc.Prof. PETRUSEL Adrian Olimpiu, Ph.D., petrusel@math.ubbcluj.ro
Aims
The aim of this course is to present basic notions and results in the field of multivalued analysis and some of their applications: operatorial inclusions, multivalued differential equations, etc.
Content
1. Functionals on the family of all nonempty subsets of a metric space.Hausdorff-Pompeiu metric
2. Continuity of multi-functions
3. Lipschitz multi-functions
4. Selection principles
5. Differentiability and integrability concepts for multi-functions
6. Fixed points results
7. Functional-differntial inclusions
References
1. J. P. Aubin, A. Cellina, Differential Inclusions, Springer, Berlin 1984
2. J. P. Aubin, H.Frankowska, Set-valued Analysis, Birkhauser, Basel, 1991
3. J. Dugundji, A. Granas, Fixed Point Theory, PWN, Warszawa, 1982
4. A. Petrusel, Multifunctii si Aplicatii, Presa Universitara Clujeana, Cluj-Napoca, 2001.
5. A. Petrusel, Operator Inclusions, Casa Cartii de Stiinta, Cluj-Napoca, 2002.
6. R.P. Agarwal, M. Meehan and D. O'Regan, Fixed point theory and applications, Cambridge Univ. Press, 2001.
7. W.A. Kirk and B. Sims (eds.), Handbook of metric fixed point theory}, Kluwer Acad. Publ., 2001.
Assessment
Exam.