Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 40A05, 26A03, 11B05

Retrieve articles in all journals with MSC (1991): 40A05, 26A03, 11B05


Additional Information

J. A. Fridy
Affiliation: Department of Mathematics, Faculty of Science, Ankara University, Ankara, 06100, Turkey
Email: fridy@mcs.kent.edu

C. Orhan
Affiliation: Department of Mathematics, Faculty of Science, Ankara University, Ankara, 06100, Turkey
Email: orhan@science.ankara.edu.tr

DOI: http://dx.doi.org/10.1090/S0002-9939-97-04000-8
PII: S 0002-9939(97)04000-8
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