Statistical (T) rates of convergence

Glasnik Matematicki, Vol. 39, No.1 (2004), 101-110.

STATISTICAL (T) RATES OF CONVERGENCE

H. I. Miller and C. Orhan

Department of Mathematics, The University of Louisville, Louisville, Kentucky, USA
University of Sarajevo, Department of Mathematics, Sarajevo, 33000, Bosnia and Herzegovina
e-mail: nmiller@utic.net.ba

Department of Mathematics, Faculty of Science, Ankara University, Tandogan 06100, Ankara, Turkey
e-mail: orhan@science.ankara.edu.tr

Abstract. The basis for comparing rates of convergence of two null sequences is that "x = (x_n) converges (stat T) faster than z = (z_n) provided that (x_n/z_n) is T-statistically convergent to zero" where T = (t_mn) is a mean. In this paper we extend the previously known results either on the ordinary convergence or statistical rates of convergence of two null sequences. We also consider lacunary statistical rates of convergence.

2000 Mathematics Subject Classification. 40A05, 40C05.

Key words and phrases. Natural density, statistically convergent sequence, rate of convergence.

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