Proceedings of the American Mathematical Society

Author(s): J. A. Fridy; C. Orhan
Journal: Proc. Amer. Math. Soc. 125 (1997), 3625-3631.
MSC (1991): Primary 40A05; Secondary 26A03, 11B05
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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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 40A05, 26A03, 11B05

J. A. Fridy
Affiliation: Department of Mathematics and Computer Science, Kent State University, Kent, Ohio 44242-0001
Email: fridy@mcs.kent.edu

J.A.Fridy and C.Orhan, Statistical Core Theorems, J.Math.Analysis and Applications 208 (1997), 520-527. (English)

Demirci,K, A-Statistical Core of a sequence, Demonstratio Mathematica (2) 23 (2000), 343-353. (English)

S.Pehlivan and M.A.Mamedov, statistical cluster points and turnpike, Optimization 48 (2000), 93-106. (English)

J.Connor, A topological and functional analytic approach to statistical convergence, Analysis of divergence, Birkhauser, Boston, 1999, pp. 403-413. (English)

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