I-convergence theorems for a class of k-positive linear operators
Mehmet Özarslan
Open Mathematics, Tome 7 (2009), p. 357-362 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 2009-01-01
EUDML-ID : urn:eudml:doc:269035 
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     author = {Mehmet \"Ozarslan},
     title = {I-convergence theorems for a class of k-positive linear operators},
     journal = {Open Mathematics},
     volume = {7},
     year = {2009},
     pages = {357-362},
     zbl = {1179.41005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0017-4}
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Mehmet Özarslan. I-convergence theorems for a class of k-positive linear operators. Open Mathematics, Tome 7 (2009) pp. 357-362. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0017-4/

[1] Devore R.A., Lorentz G.G., Constructive approximation, Springer-Verlag, Berlin, 1993 | Zbl 0797.41016

[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] | Zbl 1174.41004

[3] Duman O., Statistical approximation theorems by k-positive linear operators, Arch. Math. (Basel), 2006, 86, 569–576 [Crossref] | Zbl 1100.41012

[4] Fast H., Sur la convergence statistique, Colloquium Math., 1951, 2, 241–244 | Zbl 0044.33605

[5] Freedman A.R., Sember J.J., Densities and summability, Pacific J. Math., 1981, 95, 293–305 | Zbl 0504.40002

[6] Fridy J.A., On statistical convergence, Analysis, 1985, 5, 301–313 [Crossref] | Zbl 0588.40001

[7] Fridy J.A., Miller H.I., A matrix characterization of statistical convergence, Analysis, 1991, 11, 59–66 [Crossref] | Zbl 0727.40001

[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] | Zbl 0883.40003

[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] Kolk E., The statistical convergence in Banach spaces, Tartu Ül. Toimetised No. 928, 1991, 41–52

[11] Kostyrko P., Šalát T., Wilczyński W., I-convergence, Real Anal. Exchange, 2000/2001, 26, 669–685

[12] Kostyrko P., Mačaj M., Šalát T., Sleziak M., I-convergence and extremal I-limit points, Math. Slovaca, 2005, 55, 443–464 | Zbl 1113.40001

[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] | Zbl 0830.40002

[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] | Zbl 1148.41004

[15] Steinhaus H., Sur la convergence ordinarie et la convergence asymptotique, Colloq. Math., 1951, 2, 73–74