Local approximation properties of certain class of linear positive operators via I-convergence

• Autorzy: Mehmet Özarslan , Hüseyin Aktuǧlu
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

A-statistical convergence; I-convergence; modulus of continuity; local smoothness

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2008
• Tom: 6
• Numer: 2
• Strony: 281-286

Daty

wydano

2008-06-01

online

2008-04-15

Twórcy

autor

Mehmet Özarslan

• Eastern Mediterranean University,

autor

Hüseyin Aktuǧlu

• Eastern Mediterranean University,

Bibliografia

• [1] Devore R.A., Lorentz G.G., Constructive approximation, Springer, Berlin, 1993
• [2] Fast H., Sur la convergence statistique, Colloq. Math., 1951, 2, 241–244
• [3] Freedman A.R., Sember J.J., Densities and summability, Pacific J. Math., 1981, 95, 293–305
• [4] Fridy J.A., On statistical convergence, Analysis, 1985, 5, 301–313
• [5] Fridy J.A., Miller H.I., A matrix characterization of statistical convergence, Analysis, 1991, 11, 59–66
• [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
• [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
• [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
• [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
• [12] Steinhaus H., Sur la convergence ordinarie et la convergence asymptotique, Colloq. Math., 1951, 2, 73–74

Identyfikatory

DOI

10.2478/s11533-008-0125-6