Tbilisi Mathematical Journal

Inclusion theorems of double Deferred Cesàro means II

Richard F. Patterson, Fatih Nuray, and Metin Başarir

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


In 1932 R. P. Agnew present a definition for Deferred Cesàro mean. Using this definition R. P. Agnew present inclusion theorems for the deferred and none Deferred Cesàro means. This paper is part 2 of a series of papers that present extensions to the notion of double Deferred Cesàro means. Similar to part 1 this paper uses this definition and the notion of regularity for four dimensional matrices, to present extensions and variations of the inclusion theorems presented by R. P. Agnew in [2].

Article information

Tbilisi Math. J., Volume 9, Issue 2 (2016), 15-23.

Received: 14 March 2016
Accepted: 7 May 2016
First available in Project Euclid: 12 June 2018

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 40B05: Multiple sequences and series (should also be assigned at least one other classification number in this section)
Secondary: 40C05: Matrix methods

Double Cesàro mean Deferred Cesàro mean Double sequence $RH$-Regular Matrix $P$-convergent sequences


Patterson, Richard F.; Nuray, Fatih; Başarir, Metin. Inclusion theorems of double Deferred Cesàro means II. Tbilisi Math. J. 9 (2016), no. 2, 15--23. doi:10.1515/tmj-2016-0016. https://projecteuclid.org/euclid.tbilisi/1528769064

Export citation


  • C. R. Adams, On Summability of Double Series, Trans. Amer. Math. Soc. 34, No.2 (1932), 215–230.
  • R. P. Agnew, On Deferred Cesàro Means, Annals of Math., 33 (1932), 413–421.
  • H. J. Hamilton, Transformations of Multiple Sequences, Duke Math. Jour., 2 (1936), 29–60.
  • H. J. Hamilton, A Generalization of Multiple Sequences Transformation, Duke Math. Jour., 4 (1938), 343–358.
  • H. J. Hamilton, Change of Dimension in Sequence Transformation, Duke Math. Jour., 4 (1938), 341 - 342.
  • H. J. Hamilton, Preservation of Partial Limits in Multiple Sequence Transformations, Duke Math. Jour., 5 (1939), 293–297.
  • G. H. Hardy, Divergent Series. Oxford Univ. Press, London. 1949.
  • K. Knopp, Zur Theorie der Limitierungsverfahren (Erste Mitteilung), Math. Zeit. 31 (1930), 115–127.
  • I. J. Maddox, Some Analogues of Knopp's Core Theorem, Internat. J. Math. & Math. Sci. 2(4) (1979) 604–614. 2 (1970), 63–65.
  • R. F. Patterson, Analogues of some Fundamental Theorems of Summability Theory, Internat. J. Math. & math. Sci. 23(1), (2000), 1–9.
  • R. F. Patterson & F. Nuray, Inclusion Theorems of Double Cesáro Means, ( under consideration).
  • A. Pringsheim, Zur theorie der zweifach unendlichen zahlenfolgen, Mathematische Annalen, 53 (1900) 289-320.
  • G. M. Robison, Divergent Double Sequences and Series, Amer. Math. Soc. trans. 28 (1926) 50–73.