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Tbilisi Mathematical Journal

Editor-in-Chief: Inassaridze, Hvedri

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Mathematical Citation Quotient (MCQ) 2016: 0.14

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1512-0139
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Quasi Cauchy double sequences

Richard F. Patterson
  • Corresponding author
  • Department of Mathematics and Statistics, University of North Florida Jacksonville, Florida, 32224, USA
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Huseyin Cakalli
  • Corresponding author
  • Department of Mathematics, Maltepe University, Marmara Egitim Koyu, TR 34857, Maltepe, Istanbul, Turkey
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2015-09-21 | DOI: https://doi.org/10.1515/tmj-2015-0023

Abstract

A double sequence {xk,l} is quasi-Cauchy if given an Ɛ > 0 there exists an N ∈ N such that

We study continuity type properties of factorable double functions defined on a double subset A x A of R2 into R, and obtain interesting results related to uniform continuity, sequential continuity, continuity, and a newly introduced type of continuity of factorable double functions defined on a double subset A x A of R2 into R.

Keywords: Double sequences; P-convergent; continuity

References

  • [1] A. Alotaibi, M. Mursaleen and M. A. Alghamdi, Invariant and absolute invariant means of double sequences, J. Funct. Spaces Appl. Art. ID 465364, 9 pp., 2012. MR2923802 Web of ScienceGoogle Scholar

  • [2] D. Burton and J. Coleman, Quasi-Cauchy sequences, Amer. Math. Monthly, 117 (4), 328-333, 2010. MR 2011c:40004 Google Scholar

  • [3] H. Cakalli, Forward continuity, J. Comput. Anal. Appl. 13 (2), 225-230, 2011. MR 2012c:26004 Google Scholar

  • [4] D. Djurcic, Ljubisa D. R. Kocinac and M. R. Zizovic, Double sequences and selections, Abstr. Appl. Anal. Hindawi Publ. Corp., New York, Article Number: 497594, 2012. DOI: 10.1155/2012/497594 CrossrefGoogle Scholar

  • [5] H. Dutta, A Characterization of the class of statistically pre-Cauchy double sequences of fuzzy numbers, Appl. Math. Inf. Sci. 7 (4), 1437-1440, 2013. CrossrefGoogle Scholar

  • [6] M. Frechet, Sur quelques points du calcul fonctionnel, Rendiconti del Circolo Matematico di Palermo, 2 (2), 1-74, 1906 Google Scholar

  • [7] H. J. Hamilton, Transformations of multiple sequences, Duke Math. Jour. 2 (1), 29-60, 1936. MR1545904 CrossrefGoogle Scholar

  • [8] G. H. Hardy, On the convergence of certain multiple series, Proc. London Math. Soc., 19 s2-1 (1), 124-128, 1904. MR 1576764 CrossrefGoogle Scholar

  • [9] M. Mursaleen and S. A. Mohiuddine, Banach limit and some new spaces of double sequences, Turkish J. Math. 36 (1), 121-130, 2012. MR 2012m:46012 Google Scholar

  • [10] Richard F. Patterson, Four dimensional matrix characterization P-convergence fields of summability methods, Appl. Math. Comput. 219 (12), 6783-6791, 2013. Web of ScienceGoogle Scholar

  • [11] Richard F. Patterson, A theorem on entire four dimensional summability methods, Appl. Math. Comput. 219 (14), 7777-7782, 2013. DOI: 10.1016/j.amc.2013.02.002 Web of ScienceCrossrefGoogle Scholar

  • [12] Richard F. Patterson, Analogues of some fundamental theorems of summability theory, Inter- nat. J. Math. & Math. Sci. 23 (1), 1-9, 2000. MR 2001d:40006a Google Scholar

  • [13] Richard F. Patterson, RH-regular transformations which sums a given double sequence, Filo- mat, 27 (4), 625-627, 2013. DOI: 10.2298/FIL1304625P CrossrefGoogle Scholar

  • [14] Richard F. Patterson and E. Savas, Asymptotic equivalence of double sequences, Hacet. J. Math. Stat. 41 (4), 487-497, 2012. Google Scholar

  • [15] A. Pringsheim, Zur theorie der zweifach unendlichen zahlenfolgen, Mathematische Annalen, 53 (3), 289-321, 1900. MR 1511092 CrossrefGoogle Scholar

  • [16] G. M. Robison, Divergent double sequences and series, Amer. Math. Soc. Trans. 28 (1), 50-73, 1926. MR1501332 CrossrefGoogle Scholar

About the article

Published Online: 2015-09-21


Citation Information: Tbilisi Mathematical Journal, Volume 8, Issue 2, ISSN (Online) 1512-0139, DOI: https://doi.org/10.1515/tmj-2015-0023.

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© 2015 Richard F. Patterson, Huseyin Cakalli. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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