Abstract
References
- C¸ akan, C. and Altay, B. A class of conservative four dimensional matrices J. Ineq. Appl. Article ID 14721, 8 pages, 2006.
- C¸ akan, C., Altay, B. and Mursaleen, The σ-convergence and σ-core of double sequences, Appl. Math. Lett. 19 (10), 1122–1128, 2006.
- Cooke, R. G. Infinite Matrices and Sequence Spaces (Mcmillan, New York, 1950).
- Hamilton, H. J. Transformations of multiple sequences, Duke Math. J. 2, 29–60, 1936.
- Mishra, S. L., Satapathy, B. and Rath, N. Invariant means and σ-core, J. Indian Math. Soc. 60, 151–158, 1984.
- Moricz, F. and Rhoades, B. E. Almost convergence of double sequences and strong regularity of summability matrices, Math. Proc. Camb. Phil. Soc. 104, 283–294, 1988.
- Mursaleen Almost strongly regular matrices and a core theorem for double sequences, J. Math. Anal. Appl. 293, 523–531, 2004.
- Mursaleen and Edely, O. H. H. Almost convergence and a core theorem for double sequences, J. Math. Anal. Appl. 293, 532–540, 2004.
- Mursaleen and Sava¸s, E. Almost regular matrices for double sequences, Studia Sci. Math. Hung. 40, 205–212, 2003.
- Patterson, R. F. Double sequence core theorems, Internat. J. Math.& Math. Sci. 22, 785–793, 1999. [11] Pringsheim, A. Zur theorie der zweifach unendlichen Zahlenfolgen, Math. Ann. 53, 289–321, 1900. [12] Robinson, G. M. Divergent double sequences and series, Trans. Amer. Math. Soc. 28, 50–73, 1926.
Abstract
The famous Knopp Core of a single sequence was extended to the Pcore of a double sequence by R. F. Patterson. Recently, the MR-core and σ-core of real bounded double sequences have been introduced and some inequalities analogues to those for Knoop’s Core Theorem have been studied. The aim of this paper is to characterize a class of four-dimensional matrices, and so to obtain necessary and sufficient conditions for a new inequality related to the P- and σ-cores
Keywords
Double sequences Invariant means Core theorems and matrix transformations 2000 AMS Classification: 40 C 05
References
- C¸ akan, C. and Altay, B. A class of conservative four dimensional matrices J. Ineq. Appl. Article ID 14721, 8 pages, 2006.
- C¸ akan, C., Altay, B. and Mursaleen, The σ-convergence and σ-core of double sequences, Appl. Math. Lett. 19 (10), 1122–1128, 2006.
- Cooke, R. G. Infinite Matrices and Sequence Spaces (Mcmillan, New York, 1950).
- Hamilton, H. J. Transformations of multiple sequences, Duke Math. J. 2, 29–60, 1936.
- Mishra, S. L., Satapathy, B. and Rath, N. Invariant means and σ-core, J. Indian Math. Soc. 60, 151–158, 1984.
- Moricz, F. and Rhoades, B. E. Almost convergence of double sequences and strong regularity of summability matrices, Math. Proc. Camb. Phil. Soc. 104, 283–294, 1988.
- Mursaleen Almost strongly regular matrices and a core theorem for double sequences, J. Math. Anal. Appl. 293, 523–531, 2004.
- Mursaleen and Edely, O. H. H. Almost convergence and a core theorem for double sequences, J. Math. Anal. Appl. 293, 532–540, 2004.
- Mursaleen and Sava¸s, E. Almost regular matrices for double sequences, Studia Sci. Math. Hung. 40, 205–212, 2003.
- Patterson, R. F. Double sequence core theorems, Internat. J. Math.& Math. Sci. 22, 785–793, 1999. [11] Pringsheim, A. Zur theorie der zweifach unendlichen Zahlenfolgen, Math. Ann. 53, 289–321, 1900. [12] Robinson, G. M. Divergent double sequences and series, Trans. Amer. Math. Soc. 28, 50–73, 1926.
Details
| Primary Language | English |
|---|---|
| Subjects | Statistics |
| Journal Section | Mathematics |
| Authors | |
| Publication Date | January 1, 2009 |
| Published in Issue | Year 2009 Volume: 38 Issue: 1 |