Abstract
In this chapter, we define P-core, M-core, and R-cores by using the notion of Pringsheim’s convergence, almost convergence, and Riesz’s convergence of double sequences. We present various core theorems analogous to the well-known Knopp core theorem.
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A. Alotaibi, C. Çakan, The Riesz convergence and Riesz core of double sequences. J. Inequal. Appl. 2012, 56 (2012)
R.G. Cooke, Infinite Matrices and Sequence Spaces (Macmillan & Co., London, 1950)
H.J. Hamilton, Transformations of multiple sequences. Duke Math. J. 2, 29–60 (1936)
K. Kayaduman, C. Çakan, The Cesàro core of double sequences. Abstr. Appl. Anal. 2011, ID 950364 (2011), 9 pp.
F. Móricz, B.E. Rhoades, Almost convergence of double sequences and strong regularity of summability matrices. Math. Proc. Camb. Philos. Soc. 104, 283–294 (1988)
M. Mursaleen, Almost strongly regular matrices and a core theorem for double sequences. J. Math. Anal. Appl. 293, 523–531 (2004)
M. Mursaleen, O.H.H. Edely, Almost convergence and a core theorem for double sequences. J. Math. Anal. Appl. 293, 532–540 (2004)
M. Mursaleen, E. Savaş, Almost regular matrices for double sequences. Studia Sci. Math. Hung. 40, 205–212 (2003)
R.H. Patterson, Double sequence core theorems. Int. J. Math. Math. Sci. 22, 785–793 (1999)
G.M. Robinson, Divergent double sequences and series. Trans. Am. Math. Soc. 28, 50–73 (1926)
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Mursaleen, M., Mohiuddine, S.A. (2014). Almost Convergence and Core Theorems. In: Convergence Methods for Double Sequences and Applications. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1611-7_5
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DOI: https://doi.org/10.1007/978-81-322-1611-7_5
Publisher Name: Springer, New Delhi
Print ISBN: 978-81-322-1610-0
Online ISBN: 978-81-322-1611-7
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