On strongly deferred Cesaro summability and deferred statistical convergence of the sequences

Year 2013, Volume: 3 Issue: 1, 22 - 25, 23.06.2013

Mehmet Kucukaslan Mujde Yılmazturk

https://doi.org/10.17678/beuscitech.47136

Cited By: 1

Abstract

In this paper, it is shown that, if the sequence is strongly deferred Cesaro summable for any , then it must be deferred statistically convergent and the inverse is also satisfied when the sequence is bounded.

Keywords

Summability of sequences , strongly summable sequence , statistical convergence

References

• Agnew RP (1932). On deferred Cesaro Mean. Comm Ann Math, 33, 413-421.
• Armitage DH, Maddox IJ (1989) A new type of Cesaro Mean. Analysis 9,195-204.
• Buck RC (1953). Generalized asymptotic Density. Amer Math Comm 75, 335-346.
• Connor JS (1988). The statistical and strong p-Cesaro of sequences. Analysis 847-63.
• Connor JS (1989). On strong matrix summability with respect to a modulus and statistical convergence. Can Math Bull 32, 194-198.
• Erdös P, Tenenbaum G (1989). Sur les densites de certains suites d’entires. Proc London Math Soc 59, 417-438.
• Fast H (1951). Sur la Convergence statistique. Colloq Math 2241-244.
• Freedman AR, Sember JJ, Raphael M (1978). Some Cesaro type summability Spaces. Proc London Math Soc 37, 301-313.
• Fridy JA (1985). On statistical convergence. Analysis 5, 301-313.
• Fridy JA, Miller HI (1991). A matrix characterization of statistical convergence. Analysis 11, 59-66.
• Kucukaslan M, Yılmazturk M (2012). Deferred statistical convergence. Kyungpook Math J (Submitted).
• Maddox IJ (1967). Space of strongly summable functions. Oxford 2, Quart J Math 345-355.
• Maddox IJ (1970). Elements of Functional Analysis, Cambridge at the University Press, 208 pp.
• Mursaleen M (2000). λ-statistical convergence. Math Slavaca 50, 111-115.
• Nuray F (2010). λ-strongly summable and statistical convergence, λ-statistical convergent functions. Int J Sci Tech 34, 335-338.
• Steinhous H (1951). Sur la convergence ordinaire et la convergence asymtotique. Colloq Math 2, 73-74.
• Schoenberg IJ (1959). The integrability of certain functions and related summability methods. Amer Math Monthly 66, 361-375.
• Steinhaus H (1951). Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math., 273-74.
• Osikiewicz JA (1997). Summability of Matrix submethods and spliced sequences. PhD. Thesis, August, 90 pp.
• Zygmund A (1979). Trigonometric Series, Cambridge Univ Press, UK.