- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- 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
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 972363, 9 pages
Some Generalized Difference Sequence Spaces Defined by Ideal Convergence and Musielak-Orlicz Function
1Department of Mathematics, Faculty of Science and Arts, King Abdulaziz University (KAU), P.O. Box 80200, Khulais 21589, Saudi Arabia
2Department of Mathematics, Faculty of Science, Ain Shams University, P.O. Box 1156, Abbassia, 11566 Cairo, Egypt
3Department of Mathematics, Faculty of Education, Alzaeim Alazhari University, P.O. Box 1432, 13311 Khartoum, Sudan
Received 25 February 2013; Accepted 8 May 2013
Academic Editor: Feyzi Başar
Copyright © 2013 Awad A. Bakery 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.
- P. Kostyrko, T. Šalát, and W. Wilczyński, “On -convergence,” Real Analysis Exchange, vol. 26, no. 2, pp. 669–685, 2000-2001.
- S. Gähler, “Lineare -normierte Räume,” Mathematische Nachrichten, vol. 28, pp. 1–43, 1964.
- A. Misiak, “-inner product spaces,” Mathematische Nachrichten, vol. 140, pp. 299–319, 1989.
- H. Gunawan, “The space of -summable sequences and its natural -norm,” Bulletin of the Australian Mathematical Society, vol. 64, no. 1, pp. 137–147, 2001.
- H. Gunawan and M. Mashadi, “On -normed spaces,” International Journal of Mathematics and Mathematical Sciences, vol. 27, no. 10, pp. 631–639, 2001.
- H. Gunawan and M. Mashadi, “On finite-dimensional 2-normed spaces,” Soochow Journal of Mathematics, vol. 27, no. 3, pp. 321–329, 2001.
- E. Savaş, “-strongly summable sequences spaces in 2-normed spaces defined by ideal convergence and an Orlicz function,” Applied Mathematics and Computation, vol. 217, no. 1, pp. 271–276, 2010.
- M. Gürdal, “On ideal convergent sequences in 2-normed spaces,” Thai Journal of Mathematics, vol. 4, no. 1, pp. 85–91, 2006.
- M. Gürdal and A. Şahiner, “New sequence spaces in -normed spaces with respect to an Orlicz function,” The Aligarh Bulletin of Mathematics, vol. 27, no. 1, pp. 53–58, 2008.
- H. Nakano, “Concave modulars,” Journal of the Mathematical Society of Japan, vol. 5, pp. 29–49, 1953.
- W. H. Ruckle, “FK spaces in which the sequence of coordinate vectors is bounded,” Canadian Journal of Mathematics, vol. 25, pp. 973–978, 1973.
- I. J. Maddox, “Sequence spaces defined by a modulus,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 100, no. 1, pp. 161–166, 1986.
- J. Lindenstrauss and L. Tzafriri, “On Orlicz sequence spaces,” Israel Journal of Mathematics, vol. 10, pp. 379–390, 1971.
- M. Güngör and M. Et, “-strongly almost summable sequences defined by Orlicz functions,” Indian Journal of Pure and Applied Mathematics, vol. 34, no. 8, pp. 1141–1151, 2003.
- M. Et, Y. Altin, B. Choudhary, and B. C. Tripathy, “On some classes of sequences defined by sequences of Orlicz functions,” Mathematical Inequalities & Applications, vol. 9, no. 2, pp. 335–342, 2006.
- B. C. Tripathy, Y. Altin, and M. Et, “Generalized difference sequence spaces on seminormed space defined by Orlicz functions,” Mathematica Slovaca, vol. 58, no. 3, pp. 315–324, 2008.
- H. Kızmaz, “On certain sequence spaces,” Canadian Mathematical Bulletin, vol. 24, no. 2, pp. 169–176, 1981.
- M. Et and R. Colak, “On some generalized difference sequence spaces,” Soochow Journal of Mathematics, vol. 21, no. 4, pp. 377–386, 1995.
- B. C. Tripathy and A. Esi, “A new type of sequence spaces,” International Journal of Food Science and Technology, vol. 1, no. 1, pp. 11–14, 2006.
- B. C. Tripathy, A. Esi, and B. Tripathy, “On a new type of generalized difference Cesàro sequence spaces,” Soochow Journal of Mathematics, vol. 31, no. 3, pp. 333–340, 2005.
- L. Leindler, “Über die verallgemeinerte de la Vallée-Poussinsche Summierbarkeit allgemeiner Orthogonalreihen,” Acta Mathematica Academiae Scientiarum Hungaricae, vol. 16, no. 3-4, pp. 375–387, 1965.
- N. Şimşek, E. Savaş, and V. Karakaya, “Some geometric and topological properties of a new sequence space defined by de la Vallée-Poussin mean,” Journal of Computational Analysis and Applications, vol. 12, no. 4, pp. 768–779, 2010.
- N. Şimşek, “On some geometric properties of sequence space defined by de la Vallée-Poussin mean,” Journal of Computational Analysis and Applications, vol. 13, no. 3, pp. 565–573, 2011.
- I. J. Maddox, “On Kuttner's theorem,” Journal of the London Mathematical Society, vol. 43, pp. 285–290, 1968.
- E. Savaş, “A-sequence spaces in 2-normed space defined by ideal convergence and an Orlicz function,” Abstract and Applied Analysis, vol. 2011, Article ID 741382, 9 pages, 2011.
- M. Et, “Spaces of Cesàro difference sequences of order r defined by a modulus function in a locally convex space,” Taiwanese Journal of Mathematics, vol. 10, no. 4, pp. 865–879, 2006.