Local approximation properties of certain class of linear positive operators via I-convergence
Mehmet Özarslan ; Hüseyin Aktuǧlu
Open Mathematics, Tome 6 (2008), p. 281-286 / Harvested from The Polish Digital Mathematics Library

In this study, we obtain a local approximation theorems for a certain family of positive linear operators via I-convergence by using the first and the second modulus of continuities and the elements of Lipschitz class functions. We also give an example to show that the classical Korovkin Theory does not work but the theory works in I-convergence sense.

Publié le : 2008-01-01
EUDML-ID : urn:eudml:doc:269424
@article{bwmeta1.element.doi-10_2478_s11533-008-0125-6,
     author = {Mehmet \"Ozarslan and H\"useyin Aktu\v glu},
     title = {Local approximation properties of certain class of linear positive operators via I-convergence},
     journal = {Open Mathematics},
     volume = {6},
     year = {2008},
     pages = {281-286},
     zbl = {1148.41004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-008-0125-6}
}
Mehmet Özarslan; Hüseyin Aktuǧlu. Local approximation properties of certain class of linear positive operators via I-convergence. Open Mathematics, Tome 6 (2008) pp. 281-286. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-008-0125-6/

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

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

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

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

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

[6] 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 | Zbl 0883.40003

[7] 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 | Zbl 1039.41018

[8] Kolk E., The statistical convergence in Banach spaces, Acta Comment. Univ. Tartu. Math., 1991, 928, 41–52

[9] Kostyrko P., Mačaj M., Šalát T., I-convergence, Real Anal. Exchange, 2000, 26, 669–685

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

[11] 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 | Zbl 0830.40002

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