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Statistical Limit Superior and Limit Inferior

Authors: J. A. Fridy and C. Orhan
Journal: Proc. Amer. Math. Soc. 125 (1997), 3625-3631
MSC (1991): Primary 40A05; Secondary 26A03, 11B05
MathSciNet review: 1416085
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Abstract: Following the concept of statistical convergence and statistical cluster points of a sequence $x$, we give a definition of statistical limit superior and inferior which yields natural relationships among these ideas: e.g., $x$ is statistically convergent if and only if $\textrm{st}\text{-}\textrm{liminf} x= \textrm{st}\text{-}\textrm{limsup} x$. The statistical core of $x$ is also introduced, for which an analogue of Knopp's Core Theorem is proved. Also, it is proved that a bounded sequence that is $C_{1}$-summable to its statistical limit superior is statistically convergent.

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Additional Information

J. A. Fridy
Affiliation: Department of Mathematics, Faculty of Science, Ankara University, Ankara, 06100, Turkey

C. Orhan
Affiliation: Department of Mathematics, Faculty of Science, Ankara University, Ankara, 06100, Turkey

Keywords: Natural density, statistically convergent sequence, statistical cluster point, core of a sequence
Received by editor(s): April 20, 1995
Received by editor(s) in revised form: July 15, 1996
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1997 American Mathematical Society

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