I-convergence theorems for a class of k-positive linear operators

Mehmet Özarslan

Open Mathematics (2009)

  • Volume: 7, Issue: 2, page 357-362
  • ISSN: 2391-5455

Abstract

top
In this paper, we obtain some approximation theorems for k- positive linear operators defined on the space of analytical functions on the unit disc, via I-convergence. Some concluding remarks which includes A-statistical convergence are also given.

How to cite

top

Mehmet Özarslan. "I-convergence theorems for a class of k-positive linear operators." Open Mathematics 7.2 (2009): 357-362. <http://eudml.org/doc/269035>.

@article{MehmetÖzarslan2009,
abstract = {In this paper, we obtain some approximation theorems for k- positive linear operators defined on the space of analytical functions on the unit disc, via I-convergence. Some concluding remarks which includes A-statistical convergence are also given.},
author = {Mehmet Özarslan},
journal = {Open Mathematics},
keywords = {A-statistical convergence; I-convergence; k-positive linear operators; -statistical convergence; -convergence; -positive linear operators},
language = {eng},
number = {2},
pages = {357-362},
title = {I-convergence theorems for a class of k-positive linear operators},
url = {http://eudml.org/doc/269035},
volume = {7},
year = {2009},
}

TY - JOUR
AU - Mehmet Özarslan
TI - I-convergence theorems for a class of k-positive linear operators
JO - Open Mathematics
PY - 2009
VL - 7
IS - 2
SP - 357
EP - 362
AB - In this paper, we obtain some approximation theorems for k- positive linear operators defined on the space of analytical functions on the unit disc, via I-convergence. Some concluding remarks which includes A-statistical convergence are also given.
LA - eng
KW - A-statistical convergence; I-convergence; k-positive linear operators; -statistical convergence; -convergence; -positive linear operators
UR - http://eudml.org/doc/269035
ER -

References

top
  1. [1] Devore R.A., Lorentz G.G., Constructive approximation, Springer-Verlag, Berlin, 1993 Zbl0797.41016
  2. [2] Duman O., A Korovkin type approximation theorems via I-convergence, Czechoslovak Math. J., 2007, 57, 367–375 http://dx.doi.org/10.1007/s10587-007-0065-5[Crossref][WoS] Zbl1174.41004
  3. [3] Duman O., Statistical approximation theorems by k-positive linear operators, Arch. Math. (Basel), 2006, 86, 569–576 [Crossref] Zbl1100.41012
  4. [4] Fast H., Sur la convergence statistique, Colloquium Math., 1951, 2, 241–244 Zbl0044.33605
  5. [5] Freedman A.R., Sember J.J., Densities and summability, Pacific J. Math., 1981, 95, 293–305 Zbl0504.40002
  6. [6] Fridy J.A., On statistical convergence, Analysis, 1985, 5, 301–313 [Crossref] Zbl0588.40001
  7. [7] Fridy J.A., Miller H.I., A matrix characterization of statistical convergence, Analysis, 1991, 11, 59–66 [Crossref] Zbl0727.40001
  8. [8] Fridy J.A., Orhan C., Statistical limit superior and limit inferior, Proc. Amer. Math. Soc., 1997, 125, 3625–3631 http://dx.doi.org/10.1090/S0002-9939-97-04000-8[Crossref] Zbl0883.40003
  9. [9] Gadjiev A.D., Linear k-positive operators in a space of regular functions and theorems of P. P. Korovkin type, Izv. Akad. Nauk Azerbaĭdžan. SSR Ser. Fiz.-Tehn. Mat. Nauk, 1974, 5, 49–53 (Russian) 
  10. [10] Kolk E., The statistical convergence in Banach spaces, Tartu Ül. Toimetised No. 928, 1991, 41–52 
  11. [11] Kostyrko P., Šalát T., Wilczyński W., I-convergence, Real Anal. Exchange, 2000/2001, 26, 669–685 
  12. [12] Kostyrko P., Mačaj M., Šalát T., Sleziak M., I-convergence and extremal I-limit points, Math. Slovaca, 2005, 55, 443–464 Zbl1113.40001
  13. [13] Miller H.I., A measure theoretical subsequence characterization of statistical convergence, Trans. Amer. Math. Soc., 1995, 347, 1811–1819 http://dx.doi.org/10.2307/2154976[Crossref] Zbl0830.40002
  14. [14] Özarslan M.A., Aktuğlu H., Local approximation properties of certain class of linear positive operators via I-convergence, Cent. Eur. J. Math., 2008, 6, 281–286 http://dx.doi.org/10.2478/s11533-008-0125-6[Crossref][WoS] Zbl1148.41004
  15. [15] Steinhaus H., Sur la convergence ordinarie et la convergence asymptotique, Colloq. Math., 1951, 2, 73–74 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.