Nonlinear multivalued analysis |
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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. |