Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-26T00:23:36.539Z Has data issue: false hasContentIssue false
  • English
  • Français

On Strong Matrix Summability with Respect to a Modulus and Statistical Convergence

Published online by Cambridge University Press:  20 November 2018

Jeff Connor
Jeff Connor*
Affiliation:
Dept. of Mathematics, Ohio University, Athens, Ohio, 45701
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The definition of strong Cesaro summability with respect to a modulus is extended to a definition of strong A -summability with respect to a modulus when A is a nonnegative regular matrix summability method. It is shown that if a sequence is strongly A-summable with respect to an arbitrary modulus then it is A-statistically convergent and that Astatistical convergence and strong A-summability with respect to a modulus are equivalent on the bounded sequences.

Keywords

40D2540A05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 2 , 01 June 1989 , pp. 194 - 198
Copyright
Copyright © Canadian Mathematical Society 1989

References

1. Connor, J., The statistical and strong p-Cesaro convergence of sequences, Analysis, to appear.Google Scholar
2. Connor, J. and Loomis, I., Linear isometries on subalgebras of l∞ which contain Co, in preparation.Google Scholar
3. Connor, J., Summabillity methods associated with ideals of bounded sequences, under review.Google Scholar
4. Fast, H., Sur la convergence statistique, Colloq. Math. 2 (1951).Google Scholar
5. Flemming, R. and Jamison, J., Hermitian operators and isometries on sums ofBanach spaces, preprint.Google Scholar
6. Fridy, J., On statistical convergence, Analysis 5, 301–310.Google Scholar
7. Freedman, A. R. and Sember, J. J., Densities and summability, Pacific J. Math. 95 (1981), 293-305.Google Scholar
8. Halmos, P., Lectures on Ergodic Theory, Chelsea, 1956.Google Scholar
9. Hardy, G. H. and Littlewood, J. E., Sur la série d'une function à carré sommable, Comptes Rendus 156 (1913), 1307–9.Google Scholar
10. Leindler, L. Strong approximation by Fourier series, Akademiai Kiado, Budapest, 1985.Google Scholar
11. Maddox, I. J., Spaces of strongly summable sequences, Quart. J. Math. Oxford(2) 18 (1967) 345–55.Google Scholar
12. Maddox, I. J., Sequence spaces defined by a modulus, Math. Proc. Camb. Phil. Soc. 100 (1986), 161–66.Google Scholar
13. Salat, T. On statistically convergent sequences of real numbers, Math Solvaca 30 (2) (1980), 139–50.Google Scholar
14. Wilansky, A., Summability through functional analysis, North Holland, 1984.Google Scholar