On two classes of approximation processes of integral type


The paper aims to study two classes of linear positive operators representing modifications of Picard and Gauss operators. The new operators reproduce both constants and a given exponential function. Approximation properties in polynomial weighted spaces are investigated and the speed of convergence is measured using a certain weighted modulus of smoothness. Also, the asymptotic behavior of the integral operators are established. Finally, aspects on generalized convexity are analyzed.


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


Linear positive operator · Picard operator · Gauss operator · Weighted space · Voronovskaja formula

Paper coordinates

O. Agratini, A. Aral, E. Deniz, On two classes of approximation processes of integral type, Positivity, 21 (2017), pp. 1189-1199, https://doi.org/10.1007/s11117-016-0460-y


About this paper



Publisher Name


Print ISSN
Online ISSN

google scholar link

1. Altomare, F., Campiti, M.: Korovkin-type Approximation Theory and its Applications, de Gruyter Studies in Mathematics, vol. 17. Walter de Gruyter, Berlin (1994)
2. Butzer, P.L., Nessel, R.J.: Fourier Analysis and Approximation, Vol. I: One-Dimensional Theory. Birkhäuser, Basel (1971)
3. Gadzhiev, A.D.: Theorems of Korovkin type. Math. Notes 20(5), 995–998 (1676)
4. Ispir, N.: On modified Baskakov operators on weighted spaces. Turkish J. Math. 25, 355–365 (2001)
5. Ziegler, Z.: Linear approximation and generalized convexity. J. Approx. Theory 1, 420–443 (1968)

Related Posts