Statistical boundedness and statistical core of double sequences. (English) Zbl 1084.40001
Summary: The concept of statistical convergence was presented by Steinhaus in 1951; see H. Steinhaus [Colloq. Math. 2, 98–102 (1951; Zbl 0042.38301)]. This concept was extended to the double sequences by Mursaleen and O. H. H. Edely in [J. Math. Anal. Appl. 288, No. 1, 223-231 (2003; Zbl 1032.40001)]. Throughout this paper we will present multidimensional analogues of the results presented by J. A. Fridy and C. Orhan [Proc. Am. Math. Soc. 125, No. 12, 3625–3631 (1997; Zbl 0883.40003)]. To achieve this goal multidimensional analogues of the definition for bounded statistical sequences, statistical inferior and statistical superior will be presented. In addition to these results we will investigate statistical core for double sequences and study an inequality related to the statistical and \(P\)-cores of bounded double sequences.
References:
| [1] | Fridy, J. A.; Orhan, C., Statistical limit superior and inferior, Proc. Amer. Math. Soc., 125, 3625-3631 (1997) · Zbl 0883.40003 |
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| [3] | Mursaleen; Edely, O. H.H., Statistical convergence of double sequences, J. Math. Anal. Appl., 288, 223-231 (2003) · Zbl 1032.40001 |
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