On the Core of Double Sequences
DOI:
https://doi.org/10.5644/SJM.11.2.13Keywords:
Core of a sequence, double sequence, regular matrix, PconvergentAbstract
In this paper, we define the core of double sequences via barriers and disks. We show that these definitions are equivalent and give an inequality related to the P-core of bounded double sequences.
2010 Mathematics Subject Classification. 40B05, 40C05.
Downloads
References
J. Boos, T. Leiger and K. Zeller, Consistency theory for SM-methods, Acta Math. Hungar., 76 (1997), 83–116.
R. G. Cooke, Infinite Matrices and Sequence Spaces, Macmillan and Co. Limited, London, 1950.
C. C¸ akan and B. Altay, Statistically boundedness and statistical core of double sequences, J. Math. Anal. Appl., 317 (2006), 690–697.
A. G¨okhan, R. C¸ olak and M. Mursaleen, Some matrix transformations and generalized core of double sequences, Math. Comput. Modelling, 49 (7-8) (2009), 1721–1731.
H. J. Hamilton, Transformations of multiple of sequences, Duke Math. J., 2 (1936), 29–60.
G. H. Hardy, On the convergence of certain multiple series, Proc. Camb. Phil. Soc., 19 (1917), 86–95.
I. J. Maddox, Some analogues of Knopp’s core theorem, Int. J. Math. Math. Sci., 2 (1979), 605–614.
M. Mursaleen, Almost strongly regular matrices and a core theorem for double sequences, J. Math. Anal. Appl., 293 (2)(2004), 523–531.
M. Mursaleen and O. H. H. Edely, Almost convergence and a core theorem for double sequences, J. Math. Anal. Appl., 293 (2) (2004), 532–540.
M. Mursaleen and F. Ba¸sar, Domain of Ces`aro mean of order one in some spaces of double sequences, Studia Sci. Math. Hung., 51 (3) (2014), 335–356.
R. F. Patterson, Double sequence core theorems, Int. J. Math. Math. Sci., 22 (4) (1999), 785–793.
R. F. Patterson, Invariant core theorems for double sequences, Southeast Asian Bull. Math., 24 (3) (2000), 421–429.
R. F. Patterson, Analogues of some fundamental theorems of summability theory, Int. J. Math. Math. Sci., 23 (1) (2000), 1–9.
R. F. Patterson, Comparison theorems for four dimensional regular matrices, Southeast Asian Bull. Math., 26 (2002), 299–305.
A. Pringsheim, Elementare Theorie der unendliche Doppelreihen, Sitsungs berichte der Math. Akad. der Wissenschafftenzu M¨unch. Ber., (7) (1898), 101-153.
B. E. Rhoades, Some properties of totally coregular matrices, Illinois J. Math., 4 (1960), 518–525.
G. M. Robison, Divergent double sequences and series, Trans. Amer. Math. Soc., 28 (1) (1926), 50–73.
Y. Sever and O. Talo, ¨ e-core of double sequences, Acta Math. Hungar., 144 (1) (2014), 236–246.
A. A. Shcherbakov, Kernels of sequences of complex numbers and their regular transformations, Math. Notes, 22 (1977), 948–953.
M. Zeltser, Matrix transformations of double sequences, Acta Comment. Univ. Tartu Math., 4 (2000), 39–51.
M. Zeltser, Investigation of Double Sequence Spaces By Soft and Hard Analytical Methods, Dissertationes Mathematicae Universitatis Tartuensis 25, Tartu University Press, 2001.
M. Zeltser, On conservative matrix methods for double sequence spaces, Acta Math. Hungar., 95 (3)(2002), 225–242.
