On an approximation processes in the space of analytical functions

Akif Gadjiev; Arash Ghorbanalizadeh

Open Mathematics (2010)

  • Volume: 8, Issue: 2, page 389-398
  • ISSN: 2391-5455

Abstract

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In this paper we obtain various approximation theorems by means of k-positive linear operators defined on the space of all analytic functions on a bounded domain of the complex plane.

How to cite

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Akif Gadjiev, and Arash Ghorbanalizadeh. "On an approximation processes in the space of analytical functions." Open Mathematics 8.2 (2010): 389-398. <http://eudml.org/doc/269756>.

@article{AkifGadjiev2010,
abstract = {In this paper we obtain various approximation theorems by means of k-positive linear operators defined on the space of all analytic functions on a bounded domain of the complex plane.},
author = {Akif Gadjiev, Arash Ghorbanalizadeh},
journal = {Open Mathematics},
keywords = {The space of analytical functions; Conformal mapping; Linear k-positive operators; Korovkin type theorems; spaces of analytic functions; linear -positive operators},
language = {eng},
number = {2},
pages = {389-398},
title = {On an approximation processes in the space of analytical functions},
url = {http://eudml.org/doc/269756},
volume = {8},
year = {2010},
}

TY - JOUR
AU - Akif Gadjiev
AU - Arash Ghorbanalizadeh
TI - On an approximation processes in the space of analytical functions
JO - Open Mathematics
PY - 2010
VL - 8
IS - 2
SP - 389
EP - 398
AB - In this paper we obtain various approximation theorems by means of k-positive linear operators defined on the space of all analytic functions on a bounded domain of the complex plane.
LA - eng
KW - The space of analytical functions; Conformal mapping; Linear k-positive operators; Korovkin type theorems; spaces of analytic functions; linear -positive operators
UR - http://eudml.org/doc/269756
ER -

References

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  1. [1] Ahadov R.A., On the convergence of sequences of linear operators in a space of functions that are analytic in the disc, Izv. Akad. Nauk Azerbaidzhan. SSR Ser. Fiz.-Tekhn. Mat. Nauk, 2, 1981, 1, 67–71 (in Russian) 
  2. [2] Altomare F., Campiti M., Korovkin-type approximation theory and its applications, In: de Gruyter Studies in Mathematics, Vol. 17, Walter de Gruyter and Co, Berlin, 1994 Zbl0924.41001
  3. [3] Duman O., Statistical approximation theorems by k-positive linear operators, Arch. Math., (Basel) 86, 2006, 6, 569–576 Zbl1100.41012
  4. [4] Evgrafov M.A., The method of near systems in the space of analytic functions and its application to interpolation, Trudy Moskov. Mat. Obsc., 1956, 5, 89–201 (in Russian) 
  5. [5] Fast H., Sur la convergence statistique, Colloq. Math., 1951, 2, 241–244 (in French) Zbl0044.33605
  6. [6] Gadjiev A.D., Linear k-positive operators in a space of regular functions, and theorems of P. P. Korovkin type, Izv. Akad. Nauk Azerbaidzan. SSR Ser. Fiz.-Tehn. Mat. Nauk, 1974, 5, 49–53 (in Russian) 
  7. [7] Gadžiev A.D., A problem on the convergence of a sequence of positive linear operators on unbounded sets, and theorems that are analogous to P. P. Korovkin’s theorem, Dokl. Akad. Nauk SSSR, 218, 1974, 1001–1004 (in Russian) 
  8. [8] Gadjiev A.D., Theorems of the type of P.P. Korovkin theorems, Mat. Zametki, 1976, 20, 781–786(in Russian) 
  9. [9] Gadjiev A.D., Orhan C., Some approximation theorems via statistical convergence, Rocky Mountain J. Math., 2002, 32, 129–138 http://dx.doi.org/10.1216/rmjm/1030539612 Zbl1039.41018
  10. [10] Hacisalihoglu H.H., Gadjiev A.D., On convergence of the sequences of linear positive operators, Ankara University Press, Ankara, 1995 (in Turkish) 
  11. [11] İspir N., Convergence of sequences of k-positive linear operators in subspaces of the space of analytic functions, Hacet. Bull. Nat. Sci. Eng. Ser. B, 1999, 28, 47–53 Zbl0940.41010
  12. [12] İspir N., Atakut Ç., On the convergence of a sequence of positive linear operators on the space of m-multiple complex sequences, Hacet. Bull. Nat. Sci. Eng. Ser. B, 2000, 29, 47–54 Zbl1094.41014
  13. [13] Özarslan M.A., I-convergence theorems for a class of k-positive linear operators, Cent. Eur. J. Math., 2009, 7, 357–362 http://dx.doi.org/10.2478/s11533-009-0017-4 Zbl1179.41005

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