Characterization for the limit points of stretched double sequences

• Autorzy: Patterson R. F.
• Języki publikacji: EN

Abstrakty

EN

This paper investigates the effect of four dimensional matrix transformation on new classes of double sequences. Subsequences and stretchings of a double sequence are denned, and these definitions are used to present a four dimensional analogue of D. Dawson's Copy theorem for stretchings of a double sequence. In addition, the multidimensional analogue of D. Dawson's Copy theorem is used to characterize convergent double sequences using subsequences and stretchings.

Słowa kluczowe

EN

subseqences; Pringsheim limit point; p-convergent; p-divergent

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2002
• Tom: Vol. 35, nr 1
• Strony: 103--109
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Patterson R. F.

• Department of Mathematics and Statistics, University of North Florida, Jacksonville, Florida, 32224

Bibliografia

• [1] D. F. Dawson, Summability of Subsequences and Stretchings of Sequences, Pacific J. Math. 44 (1973), 455-460.
• [2] H. J. Hamilton, Transformations of Multiple Sequences, Duke Math. J. 2 (1936), 29-60.
• [3] R. F. Patterson, Analogues of some Tauberian Theorems for Stretchings, to be published in the International Journal of Mathematics and Mathematics Sciences.
• [4] R. F. Patterson, A characterization for the limit points of double sequences, Demonstratio Math. 32(4) (1999), 775-780.
• [5] A. Pringsheim, Zur theorie der zweifach unendlichen Zahlenfolgen, Mathematische Annalen, 53 (1900), 289-321.
• [6] G. M. Robison, Divergent Double Sequences and Series, Amer. Math. Soc. trans. 28 (1926), 50-73.