INCLUSION THEOREMS DOUBLE DEFERRED CESARO MEANS III
Abstract
R. P. Agnew presents a definition for Deferred Cesaro mean. Using this definition R. P. Agnew presents inclusion theorems for the deferred and none Deferred Cesaro means. This paper is part III of a series of papers that present extensions to the notion of double Deferred Cesaro means. Similar to the part I [11] and the part 2 [12] this paper uses these definitions and the notion of regularity for four-dimensional matrices, to present a multidimensional inclusion theorem and a multidimensional equivalent theorem, which are the multidimensional analog of R. P. Agnew's results in [2].
Keywords
Full Text:
PDFReferences
C. R. Adams, On Summability of Double Series, Trans. Amer. Math. Soc. 34, No.2 1932, 215-230.
R. P. Agnew, On Deferred Cesaro 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.
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 Cesaro Means, ( under consideration).
R. F. Patterson, F. Nuray, & M. Basarır, Inclusion Theorems of Double Cesaro Means II, Tbilisi Mathematical Journal 9(2) (2016), 15-23.
A. Pringsheim, Zur theorie der zweifach unendlichen zahlenfolgen, Mathematische Annalen, 53 (1900) 289 - 321.
G. M. Robison, Divergent Double Sequences and Series, Amer. Math. Soc. trans. 28 (1926) 50 - 73.
DOI: https://doi.org/10.22190/FUMI220128065P
Refbacks
- There are currently no refbacks.
ISSN 0352-9665 (Print)