Modular Spaces Topology

Author(s)
Ahmed Hajji

ABSTRACT

In this paper, we present and discuss the topology of modular spaces using the filter base and we then characterize closed subsets as well as its regularity.

Cite this paper

A. Hajji, "Modular Spaces Topology,"*Applied Mathematics*, Vol. 4 No. 9, 2013, pp. 1296-1300. doi: 10.4236/am.2013.49175.

A. Hajji, "Modular Spaces Topology,"

References

[1] J. Musielak, “Orlicz Spaces and Modular Spaces,” Lecture Notes in Mathematics, Vol. 1034, 1983.

[2] A. Ait Taleb and E. Hanebaly, “A Fixed Point Theorem and Its Application to Integral Equations in Modular Function Spaces,” Proceedings of the American Mathematical Society, Vol. 128, 2000, pp. 419-426. doi:10.1090/S0002-9939-99-05546-X

[3] A. Razani and R. Moradi, “Common Fixed Point Theorems of Integral Type in Modular Spaces,” Bulletin of the Iranian Mathematical Society, Vol. 35, No. 2, 2009, pp. 11-24.

[4] A. Razani, E. Nabizadeh, M. B. Mohammadi and S. H. Pour, “Fixed Point of Nonlinear and Asymptotic Contractions in the Modular Space,” Abstract and Applied Analysis, Vol. 2007, 2007, Article ID: 40575.

[5] A. P. Farajzadeh, M. B. Mohammadi and M. A. Noor, “Fixed Point Theorems in Modular Spaces,” Mathematical Communications, Vol. 16, 2011, pp. 13-20.

[6] M. A. Khamsi, “Nonlinear Semigroups in Modular Function Spaces,” Thèse d'état, Département de Mathématiques, Rabat, 1994.

[7] M. A. Khamsi, W. Kozlowski and S. M.-Reich, “Fixed Point Theory in Modular Function Spaces,” Nonlinear Analysis, Theory, Methods and Applications, Vol. 14, No. 11, 1990, pp. 935-953.

[8] F. Lael and K. Nourouzi, “On the Fixed Points of Correspondences in Modular Spaces,” ISRN Geometry, Vol. 2011, 2011, Article ID: 530254. doi:10.5402/2011/530254

[9] M. A. Khamsi, “Quasicontraction Mappings in Modular Spaces without Δ2-Condition,” Fixed Point Theory and Applications, Vol. 2008, 2008, Article ID: 916187.

[10] A. Hajji, “Forme Equivalente à la Condition Δ2 et Certains Résultats de Séparations dans les Espaces Modulaires,” 2005. http://arXiv.org/abs/math.FA/0509482

[1] J. Musielak, “Orlicz Spaces and Modular Spaces,” Lecture Notes in Mathematics, Vol. 1034, 1983.

[2] A. Ait Taleb and E. Hanebaly, “A Fixed Point Theorem and Its Application to Integral Equations in Modular Function Spaces,” Proceedings of the American Mathematical Society, Vol. 128, 2000, pp. 419-426. doi:10.1090/S0002-9939-99-05546-X

[3] A. Razani and R. Moradi, “Common Fixed Point Theorems of Integral Type in Modular Spaces,” Bulletin of the Iranian Mathematical Society, Vol. 35, No. 2, 2009, pp. 11-24.

[4] A. Razani, E. Nabizadeh, M. B. Mohammadi and S. H. Pour, “Fixed Point of Nonlinear and Asymptotic Contractions in the Modular Space,” Abstract and Applied Analysis, Vol. 2007, 2007, Article ID: 40575.

[5] A. P. Farajzadeh, M. B. Mohammadi and M. A. Noor, “Fixed Point Theorems in Modular Spaces,” Mathematical Communications, Vol. 16, 2011, pp. 13-20.

[6] M. A. Khamsi, “Nonlinear Semigroups in Modular Function Spaces,” Thèse d'état, Département de Mathématiques, Rabat, 1994.

[7] M. A. Khamsi, W. Kozlowski and S. M.-Reich, “Fixed Point Theory in Modular Function Spaces,” Nonlinear Analysis, Theory, Methods and Applications, Vol. 14, No. 11, 1990, pp. 935-953.

[8] F. Lael and K. Nourouzi, “On the Fixed Points of Correspondences in Modular Spaces,” ISRN Geometry, Vol. 2011, 2011, Article ID: 530254. doi:10.5402/2011/530254

[9] M. A. Khamsi, “Quasicontraction Mappings in Modular Spaces without Δ2-Condition,” Fixed Point Theory and Applications, Vol. 2008, 2008, Article ID: 916187.

[10] A. Hajji, “Forme Equivalente à la Condition Δ2 et Certains Résultats de Séparations dans les Espaces Modulaires,” 2005. http://arXiv.org/abs/math.FA/0509482