Journal Menu
- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Journal of Function Spaces and Applications
Volume 2012 (2012), Article ID 465364, 9 pages
doi:10.1155/2012/465364
Research Article
Invariant and Absolute Invariant Means of Double Sequences
1Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
2Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
Received 20 February 2012; Revised 17 April 2012; Accepted 28 April 2012
Academic Editor: Sivaram K. Narayan
Copyright © 2012 Abdullah Alotaibi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Linked References
- F. Móricz, “Extensions of the spaces c and co from single to double sequences,” Acta Mathematica Hungarica, vol. 57, no. 1-2, pp. 129–136, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- A. Pringsheim, “Zur Theorie der zweifach unendlichen Zahlenfolgen,” Mathematische Annalen, vol. 53, no. 3, pp. 289–321, 1900. View at Publisher · View at Google Scholar
- H. J. Hamilton, “Transformations of multiple sequences,” Duke Mathematical Journal, vol. 2, no. 1, pp. 29–60, 1936. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- M. Mursaleen and S. A. Mohiuddine, “Almost bounded variation of double sequences and some four dimensional summability matrices,” Publicationes Mathematicae Debrecen, vol. 75, no. 3-4, pp. 495–508, 2009.
- G. M. Robison, “Divergent double sequences and series,” Transactions of the American Mathematical Society, vol. 28, no. 1, pp. 50–73, 1926. View at Publisher · View at Google Scholar
- M. Mursaleen, “On 𝒜-invariant mean and 𝒜-almost convergence,” Analysis Mathematica, vol. 37, no. 3, pp. 173–180, 2011. View at Publisher · View at Google Scholar
- P. Schaefer, “Infinite matrices and invariant means,” Proceedings of the American Mathematical Society, vol. 36, pp. 104–110, 1972. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- M. Mursaleen, “On some new invariant matrix methods of summability,” The Quarterly Journal of Mathematics, vol. 34, no. 133, pp. 77–86, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- M. Mursaleen and S. A. Mohiuddine, “Some inequalities on sublinear functionals related to the invariant mean for double sequences,” Mathematical Inequalities & Applications, vol. 13, no. 1, pp. 157–163, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- M. Mursaleen and S. A. Mohiuddine, “Banach limit and some new spaces of double sequences,” Turkish Journal of Mathematics, vol. 36, pp. 121–130, 2012.
- C. Çakan, B. Altay, and M. Mursaleen, “The σ-convergence and σ-core of double sequences,” Applied Mathematics Letters, vol. 19, no. 10, pp. 1122–1128, 2006. View at Publisher · View at Google Scholar
- C. Çakan, B. Altay, and H. Coşkun, “σ-regular matrices and a σ-core theorem for double sequences,” Hacettepe Journal of Mathematics and Statistics, vol. 38, no. 1, pp. 51–58, 2009.
- M. Mursaleen and S. A. Mohiuddine, “Double σ-multiplicative matrices,” Journal of Mathematical Analysis and Applications, vol. 327, no. 2, pp. 991–996, 2007. View at Publisher · View at Google Scholar
- M. Mursaleen and S. A. Mohiuddine, “Regularly σ-conservative and σ-coercive four dimensional matrices,” Computers & Mathematics with Applications, vol. 56, no. 6, pp. 1580–1586, 2008. View at Publisher · View at Google Scholar
- M. Mursaleen and S. A. Mohiuddine, “On σ-conservative and boundedly σ-conservative four-dimensional matrices,” Computers & Mathematics with Applications, vol. 59, no. 2, pp. 880–885, 2010. View at Publisher · View at Google Scholar
- M. Mursaleen and S. A. Mohiuddine, “Invariant mean and some core theorems for double sequences,” Taiwanese Journal of Mathematics, vol. 14, no. 1, pp. 21–33, 2010. View at Zentralblatt MATH
- 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- G. G. Lorentz, “A contribution to the theory of divergent sequences,” Acta Mathematica, vol. 80, pp. 167–190, 1948. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- M. Mursaleen, “Matrix transformations between some new sequence spaces,” Houston Journal of Mathematics, vol. 9, no. 4, pp. 505–509, 1983. View at Zentralblatt MATH
- G. Das and S. K. Sahoo, “A generalisation of strong and absolute almost convergence,” The Journal of the Indian Mathematical Society, vol. 58, no. 1–4, pp. 65–74, 1992. View at Zentralblatt MATH
- G. Das and B. K. Ray, “Absolute almost convergence and application,” in Modern Methods of Analysis and Its Applications, M. Mursaleen, Ed., pp. 11–20, Anamaya, New Delhi, India, 2010.
- M. Mursaleen and S. A. Mohiuddine, “Some new double sequence spaces of invariant means,” Glasnik Matematički, Serija III, vol. 45, no. 65, pp. 139–153, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- G. Das and B. Kuttner, “Space of absolute almost convergence,” Indian Journal of Mathematics, vol. 28, no. 3, pp. 241–257, 1986.