Approximation properties of a class of linear operators


This work focuses on a class of linear positive operators of discrete type. We present the relationship between the local smoothness of functions and the local approximation. Also, the degree of approximation in terms of the moduli of smoothness is established, and the statistical convergence of the sequence is studied.


Octavian Agratini
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania


linear positive operator; moduli of smoothness; K-functional; statistical convergence

Paper coordinates

O. Agratini, Approximation properties of a class of linear operators, Mathematical Methods in the Applied Sciences, 36 (2013) no. 17, pp. 2353-2358.


requires subscription:

About this paper


Mathematical Methods in the Applied Sciences

Publisher Name

John Wiley & Sons

Print ISSN


Online ISSN


google scholar link

1. Jain GC. Approximation of functions by a new class of linear operators. Journal of the AustralianMathematical Society 1972; 13(3):271–276.
2. Mirakjan GM. Approximation of continuous functions with the aid of polynomials. Doklady Akademii Nauk SSSR 1941; 31:201–205. (in Russian).
3. Szász O. Generalization of S. Bernstein’s polynomials to the infinite interval. Journal of Research of the National Bureau of Standards1950; 45:239–245.
4. Peetre J. A theory of interpolation of normed spaces. Notas deMatematica, Rio de Janeiro 1968; 39:1–86.
5. Johnen H. Inequalities connected withmoduli of smoothness. Matematicki Vesnik 1972; 9(24):289–303.
6. Fast H. Sur le convergence statistique. ColloquiumMathematicum 1951; 2:241–244.
7. Gadjiev AD, Orhan C. Some approximation theorems via statistical convergence. RockyMountain Journal of Mathematics 2002; 32:129–138.
8. Kirov G, Popova L. A generalization of the linear positive operators. Mathematica Balkanica 1993; 2:149–162.
9. Agratini O. Statistical convergence of a non-positive approximation process. Chaos, Solitons & Fractals 2011; 44:977–981.

Related Posts