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

SUBJECT

Code
Subject
MMN0004 The Theory of Linear Operators
Section
Semester
Hours: C+S+L
Category
Type
Mathematics - in Romanian
6
2+1+0
speciality
optional
Applied Mathematics
6
2+1+0
speciality
optional
Teaching Staff in Charge
Prof. AGRATINI Octavian, Ph.D.,  agratinimath.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
Bohman-Korovkin theorems. Moduli of smoothness. Rate of convergence.
Toeplitz theorem. The construction of linear operators by using summation methods: Cesaro, Euler, Hausdorff, Jakimovski, Meir-Sharma.
The construction of linear positive operators by probabilistic methods. The study of some classical operators: Bernstein, Bleimann-Butzer-Hahn, Baskakov, Feller, Favard-Szasz, Meyer-Konig-Zeller, Weierstrass.
Stancu operators defined by using Markov-Polya probabilistic scheme.
Generalization of discrete operators to integral form in Kantorovich and Durrmeyer sense.
Binomial type operators and their applications to approximation of functions.
Linear operators introduced via q-Calculus. Examples of q-operators. Characteristic properties.
References
[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] KAC, V., CHEUNG, P., Quantum Calculus, Universitext, Springer-Verlag, New York, 2002.
[7] 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 1/3 and
2/3, respectively.
Links: Syllabus for all subjects
Romanian version for this subject
Rtf format for this subject