On asymptotically statistical equivalent sequences

• Autorzy: Patterson R. F.
• Języki publikacji: EN

Abstrakty

EN

This paper presents the following definition which is a natural combination of the definition for Asymptotically equivalent and Statistically limit. Two nonnegative sequences [x] and [y] are said to be asymptotically statistical equivalents of multiple L provided that for every e > 0, limn 1/n{the number of k < n : |xk/yk-L\ > e} = 0 (denoted by x Sl y), and simply asymptotically statistical equivalent if L = 1. In addition, there are also statistical analogs of theorems of Poyvanents in [5].

Słowa kluczowe

EN

Pringsheim limit point; p-convergent

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2003
• Tom: Vol. 36, nr 1
• Strony: 149--153
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Patterson R. F.

• Department of Mathematics and Statistics, University of North Florida, Building 11, Jacksonville, Florida, 32224

Bibliografia

• [1] J. A. Fridy, Minimal rates of summability, Canad. J. Math., 30(4) (1978) 808-816.
• [2] J. A. Fridy, On statistical convergence, Analysis 5 (1985), 301-313.
• [3] M. Marouf, Summability matrices that preserve various types of sequential equivalence, Kent State University, Mathematics.
• [4] R. F. Patterson, Some characterization of asymptotic equivalent double sequences, to be published in the Soochow Journal of Mathematics.
• [5] I. P. Pobyvanets, Asymptotic equivalence of some linear transformations defined by a nonnegative matrix and reduced to generalized equivalence on the sense of Cesàro and Abel, Mat. Fiz. 28 (1980), 83-87, 123.