Modular Spaces Topology
, PP. 1296-1300 10.4236/am.2013.49175
Keywords: Topology of Modular Spaces, Δ, 2-Condition Filter Base
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.
[ 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.
[ 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.
[ 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
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