SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2012 / Cilt: 41 - Sayı: 4

Asymptotic equivalence of double sequences

F. Richard PATTERSON
Ekrem SAVAS
Pages
487–497
Publication Date
2022-10-18
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Using this notion necessary and sufficient conditions on the entries of a four-dimensional matrix are given to ensure that the transformation will preserve asymptotic equivalence.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The goal of this paper is to present a four-dimensional matrix char- acterization of asymptotic equivalence of double sequences.
📊
Key Findings & Data:Two double sequences are asymptotic equivalent if and only if P − $lim_{k,l}frac{x_k,l}{y_k,l}$ = 1, where x and y are selected judicially.
💡
Conclusion & Impact:Using this notion necessary and sufficient conditions on the entries of a four-dimensional matrix are given to ensure that the transformation will preserve asymptotic equivalence.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

The goal of this paper is to present a four-dimensional matrix char- acterization of asymptotic equivalence of double sequences. This will be accomplished with the following notion of asymptotic equivalence of double sequences. Two double sequences are asymptotic equivalent if and only if P − $lim_{k,l}frac{x_k,l}{y_k,l}$ = 1, where x and y are selected judicially. Using this notion necessary and sufficient conditions on the entries of a four-dimensional matrix are given to ensure that the transformation will preserve asymptotic equivalence.

🔖

Cite This Article

PATTERSON, F. R., SAVAS, E. (2022). Asymptotic equivalence of double sequences. Hacettepe Journal of Mathematics and Statistics, Cilt: 41 - Sayı: 4, 487–497. https://ajindex.com/articles/530499

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (11)

  1. Fridy, J.A. Minimal rate of summability, Can. J. Math. XXX(4), 808–816, 1978
  2. Hamilton, H. J. Transformations of multiple sequences, Duke Math. J. 2, 29–60, 1936
  3. Hardy, G.H. Divergent Series (Oxford University Press, London, 1949)
  4. Li, J. Asymptotic equivalence of sequences and summability, Internat. J. Math. & Math. Sci. 20 (4), 749–758, 1997
  5. Marouf, M. Summability Matrices that Preserve Various Types of Sequential Equivalence (Kent State University, Mathematics, 1992)
  6. Patterson, R. F. Some characterization of asymptotic equivalent double sequences, in press
  7. Patterson, R. F. Rates of convergence for double sequences, Southeast Asian Bull. Math. 26 (3), 469–478, 2002
  8. Patterson, R.F. Analogues of some fundamental theorems of summability theorey, Internat. J. Math. & Math. Sci. 23 (1), 1–9, 2000
  9. Pobyvanets, I. P. Asymptotic equivalence of some linear transformations defined by a non- negative matrix and reduced to generalized equivalence on the sense of Ces`aro and Abel, Mat. Fiz. 28 (123), 83–87, 1980
  10. Pringsheim, A. Zur theorie der zweifach unendlichen zahlenfolgen, Mathematische Annalen 53, 289–321, 1900
  11. Robison, G.M. Divergent double sequences and series, Amer. Math. Soc. Trans. 28, 50–73, 1936.