A note on four dimensional summability methods
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
Ishiguro studied some two dimensional summability methods in [7]. In this paper, we define the four dimensional Zweier matrix and extend the results given by Ishiguro [7] to four dimensional summability methods. We prove that an Abel summable double sequence is also summable the product of Abel and Zweier meth- ods to the same limit. Besides this, we show the four dimensional Riesz and Zweier methods don’t imply each other. In addition, we emphasize the four dimensional Zweier method implies the four dimensional Borel method.
Abstract
Ishiguro studied some two dimensional summability methods in [7]. In this paper, we define the four dimensional Zweier matrix and extend the results given by Ishiguro [7] to four dimensional summability methods. We prove that an Abel summable double sequence is also summable the product of Abel and Zweier meth- ods to the same limit. Besides this, we show the four dimensional Riesz and Zweier methods don’t imply each other. In addition, we emphasize the four dimensional Zweier method implies the four dimensional Borel method.
참고문헌 (19)
- A. M. Alotaibi, "The Riesz convergence and Riesz core of double sequences", J. Inequal. Appl, 56, pp.8~ (2012)[DOI]
- F. Basar, "Summability theory and its applications", pp.27~492 (2022), CRC Press
- F. Basar, "Double sequence spaces and four-dimensional matrices", pp.18~233 (2022), CRC Press
- S. Demiriz, "Domain of Euler-Totient matrix operator in the space Lp", Korean J. Math, 28(2), pp.361~378 (2020)[DOI]
- S. Demiriz, "The spaces of almost Euler-Totient convergent and almost Euler-Totient null double sequences", Ann. Oradea Univ. Math. Fascicola, 28(2), pp.21~32 (2021)
- H. J. Hamilton, "Transformations of multiple sequences", Duke Math. J, 2, pp.29~60 (1936)[DOI]
- K. Ishiguro, "On the summability method(Y)", Proc. Japan Acad, 40(7), pp.482~486 (1964)[DOI]
- M. T. Karaev, "On Abel convergence of double sequences", Numer. Funct. Anal. Optim, 31(10), pp.1185~1189 (2010)[DOI]
- A. Kiltho, "Some double sequence spaces generated by four-dimensional Pascal matrix", Int. J. Math. Comput. Res, 9(8), pp.2371~2375 (2021)[DOI]
- A. Kiltho, "On the domain of four dimensional Pascal matrix in the space l2q", Int. J. Sci. Research Publ, 11(9), pp.288~292 (2021)
- M. Mursaleen, "Domain of Cesaro mean of order one in some spaces of double sequences", Stud. Sci. Math. Hungar, 51(3), pp.335~356 (2014)[DOI]
- F. Nuray, "Some Tauberian theorems for four-dimensional Euler and Borel summability", Adv. Dierence Equ, 50, pp.8~ (2015)
- A. Pringsheim, "Zur theorie der zweifach unendlichen Zahlenfolgen", Math. Ann, 53, pp.289~321 (1900)[DOI]
- G. M. Robison, "Divergent double sequences and series", Trans. Amer. Math. Soc, 28, pp.50~73 (1926)[DOI]
- O. Szasz, "On the product of two summability methods", Ann. Soc. Polon. Math, 25, pp.75~84 (1952)
- G. Talebi, "Operator norms of four-dimensional Hausdor matrices on the double Euler sequence spaces", Linear Multilinear Algebra, 65(11), pp.2257~2267 (2017)[DOI]
- G. Talebi, "Boundedness problem of four-dimensional matrices on the domain spaces of Lp", Results Math, 74(1), pp.1~16 (2019)[DOI]
- M. Yesilkayagꠕl, "Domain of Euler mean in the space of absolutely p-summable double sequences with 0 < p < 1", Anal. Theory Appl, 34(3), pp.241~252 (2018)[DOI]
- M. Yesilkayagꠕl, "Domain of Riesz mean in some spaces of double sequences", Indag. Math. (N. S. ), 29(3), pp.1009~1029 (2018)[DOI]