Abstract and Applied Analysis

Almost Conservative Four-Dimensional Matrices through de la Vallée-Poussin Mean

S. A. Mohiuddine and Abdullah Alotaibi

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Abstract

The purpose of this paper is to generalize the concept of almost convergence for double sequence through the notion of de la Vallée-Poussin mean for double sequences. We also define and characterize the generalized regularly almost conservative and almost coercive four-dimensional matrices. Further, we characterize the infinite matrices which transform the sequence belonging to the space of absolutely convergent double series into the space of generalized almost convergence.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 412974, 6 pages.

Dates
First available in Project Euclid: 26 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1395858508

Digital Object Identifier
doi:10.1155/2014/412974

Mathematical Reviews number (MathSciNet)
MR3166610

Zentralblatt MATH identifier
07022344

Citation

Mohiuddine, S. A.; Alotaibi, Abdullah. Almost Conservative Four-Dimensional Matrices through de la Vallée-Poussin Mean. Abstr. Appl. Anal. 2014 (2014), Article ID 412974, 6 pages. doi:10.1155/2014/412974. https://projecteuclid.org/euclid.aaa/1395858508


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References

  • S. Banach, Théorie des Operations Lineaires, 1932.
  • G. G. Lorentz, “A contribution to the theory of divergent sequences,” Acta Mathematica, vol. 80, pp. 167–190, 1948.
  • S. A. Mohiuddine, “An application of almost convergence in approximation theorems,” Applied Mathematics Letters, vol. 24, no. 11, pp. 1856–1860, 2011.
  • F. Móricz and B. E. Rhoades, “Almost convergence of double sequences and strong regularity of summability matrices,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 104, no. 2, pp. 283–294, 1988.
  • M. Mursaleen and S. A. Mohiuddine, “Banach limit and some new spaces of double sequences,” Turkish Journal of Mathematics, vol. 36, no. 1, pp. 121–130, 2012.
  • M. Başarir, “On the strong almost convergence of double sequences,” Periodica Mathematica Hungarica, vol. 30, no. 3, pp. 177–181, 1995.
  • F. Başar and M. Kirişçi, “Almost convergence and generalized difference matrix,” Computers & Mathematics with Applications, vol. 61, no. 3, pp. 602–611, 2011.
  • F. Čunjalo, “Almost convergence of double subsequences,” Filomat, vol. 22, no. 2, pp. 87–93, 2008.
  • K. Kayaduman and C. Çakan, “The cesáro core of double sequences,” Abstract and Applied Analysis, vol. 2011, Article ID 950364, 9 pages, 2011.
  • Mursaleen, “Almost strongly regular matrices and a core theorem for double sequences,” Journal of Mathematical Analysis and Applications, vol. 293, no. 2, pp. 523–531, 2004.
  • Mursaleen and O. H. H. Edely, “Almost convergence and a core theorem for double sequences,” Journal of Mathematical Analysis and Applications, vol. 293, no. 2, pp. 532–540, 2004.
  • M. Zeltser, M. Mursaleen, and S. A. Mohiuddine, “On almost conservative matrix methods for double sequence spaces,” Publicationes Mathematicae Debrecen, vol. 75, no. 3-4, pp. 387–399, 2009.
  • A. Pringsheim, “Zur theorie der zweifach unendlichen zahlenfolgen,” Mathematische Annalen, vol. 53, no. 3, pp. 289–321, 1900.
  • B. Altay and F. Başar, “Some new spaces of double sequences,” Journal of Mathematical Analysis and Applications, vol. 309, no. 1, pp. 70–90, 2005.
  • H. J. Hamilton, “Transformations of multiple sequences,” Duke Mathematical Journal, vol. 2, no. 1, pp. 29–60, 1936.
  • S. A. Mohiuddine and A. Alotaibi, “Some spaces of double sequences obtained through invariant mean and related concepts,” Abstract and Applied Analysis, vol. 2013, Article ID 507950, 11 pages, 2013.
  • Mursaleen and S. A. Mohiuddine, “Double $\sigma $-multiplicative matrices,” Journal of Mathematical Analysis and Applications, vol. 327, no. 2, pp. 991–996, 2007.
  • M. Mursaleen and S. A. Mohiuddine, “On $\sigma $-conservative and boundedly $\sigma $-conservative four-dimensional matrices,” Computers & Mathematics with Applications, vol. 59, no. 2, pp. 880–885, 2010.
  • P. Schaefer, “Infinite matrices and invariant means,” Proceedings of the American Mathematical Society, vol. 36, pp. 104–110, 1972.
  • G. M. Robison, “Divergent double sequences and series,” Transactions of the American Mathematical Society, vol. 28, no. 1, pp. 50–73, 1926.
  • J. P. King, “Almost summable sequences,” Proceedings of the American Mathematical Society, vol. 17, pp. 1219–1225, 1966.
  • P. Schaefer, “Matrix transformations of almost convergent sequences,” Mathematische Zeitschrift, vol. 112, pp. 321–325, 1969.
  • F. Başar and I. Solak, “Almost-coercive matrix transformations,” Rendiconti di Matematica e delle sue Applicazioni, vol. 11, no. 2, pp. 249–256, 1991.
  • F. Móricz, “Extensions of the spaces $c$ and ${c}_{0}$ from single to double sequences,” Acta Mathematica Hungarica, vol. 57, no. 1-2, pp. 129–136, 1991.
  • M. Mursaleen and S. A. Mohiuddine, “Regularly $\sigma $-conservative and $\sigma $-coercive four dimensional matrices,” Computers & Mathematics with Applications, vol. 56, no. 6, pp. 1580–1586, 2008.
  • C. Eizen and G. Laush, “Infinite matrices and almost convergence,” Mathematica Japonica, vol. 14, pp. 137–143, 1969. \endinput