Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Graduate
SUBJECT

Code	Subject	
MMN0004	Linear Approximation Processes	

Section	Semester	Hours: C+S+L	Category	Type	
Mathematics-Computer Science - in Romanian	5	2+1+0	speciality	optional	

Teaching Staff in Charge	Prof. AGRATINI Octavian, Ph.D., agratini@math.ubbcluj.ro	
Aims	The course provides the students with the best-known applications of Korovkin-type approximation theory and determines fruitful directions for future advanced study.
 Knowing and approaching the construction methods of approximation operators.
 Knowing the most recent results obtained about the generalizations of some classical approximation operators.	
Content	Convolution products and linear positive operators.
The construction of linear operators by using summation methods: Cesaro, Euler, Hausdorff, Jakimovski.
The construction of linear positive operators by probabilistic methods. The study of some classical operators: Bernstein, Baskakov, Feller, Favard-Szasz, Meyer-Konig and Zeller, Weierstrass.
Stancu, Bleimann, Butzer and Hahn operators.
Generalization of discrete operators to integral form in Kantorovich and Durrmeyer sense.
Altomare projections and applications.
Approximation of high order convex functions. Semigroups of operators.
Binomial type operators and applications.  	
Bibliography	[1] AGRATINI, O., Aproximare prin operatori liniari, Presa Universitară Clujeană, 2000.
[2] ALTOMARE, F., CAMPITI, M., Korovkin-type Approximation Theory and its Applications,  Walter de Gruyter, Berlin-New York, 1994.
[3] ANASTASSIOU, G.A., GAL, S.G., Approximation Theory. Moduli of Continuity and Global Smoothness Preservation, Birkauser, Boston, 2000.
[4] BENNETT, C., SHARPLEY, R., Interpolation of Operators, Academic Press, Inc., New York, 1998.
[5] DITZIAN, Z., TOTIK, V., Moduli of Smoothness, Springer Series in Computation Mathematics, Vol. 9, Springer-Verlag, New York Inc., 1987.
[6] STANCU, D.D., COMAN, GH., AGRATINI, O., TRIMBITAS, R., Analiză numerică şi teoria aproximării, Vol.I, Presa Universitară Clujeană, 2001.
	
Assessment	During the semester: a Control Paper.
In the session: written exam.
The final grade: arithmetic mean of the above 2 marks having the weights 1 and
2, respectively.