SIFAT TERBATAS MODULAR PADA RUANG BARISAN ORLICZ
Keywords:
fungsi Orlicz, modular, terbatasAbstract
Dalam makalah ini dikonstruksi topologi pada ruang barisan Orliz dengan menggunakan persekitaran modular titik nol. Persekitaran tersebut memimiliki sifat seimbang, menyerap dan simetris. Dengan menggunakan persekitaran tersebut, sifat-sifat barisan konvergen modular dan himpunan terbatas modular ditelaah. Selanjutnya diperolehnya hubungan antara himpunan terbatas modular dan himpunan barisan konvergen modular.
References
M. A. Khamsi, “A convexity property in Modular function spaces.”
E. Malkowsky and V. Veličković, “Topologies of some new sequence spaces, their duals, and the graphical representations of neighborhoods,” Topol Appl, vol. 158, no. 12, pp. 1369–1380, Aug. 2011, doi: 10.1016/j.topol.2011.05.011.
E. Kolk, “Topologies in generalized orlicz sequence spaces,” Filomat, vol.25, no. 4, pp. 191–211, Dec. 2011, doi: 10.2298/FIL1104191K.
V. V. Chistyakov, “A fixed point theorem for contractions in modular metric spaces,” Dec. 2011, doi: 10.1007/978-1-4614-5574-5_4.
H. Abobaker and R. A. Ryan, “Modular Metric Spaces,” Mar. 2022, [Online]. Available: http://arxiv.org/abs/2203.12359
M. M. Jabber and N. F. Al-Mayahi, “Weak∗ topology on modular space and some properties,” in Journal of Physics: Conference Series, IOP Publishing Ltd, Aug. 2020. doi: 10.1088/1742-6596/1591/1/012070.
A. Hajji, “Modular Spaces Topology,” Appl Math (Irvine), vol. 04, no. 09, pp. 1296–1300, 2013, doi: 10.4236/am.2013.49175.
W. M. Kozlowski, “Advancements in fixed point theory in modular function spaces,” Arabian Journal of Mathematics, vol. 1, no. 4, pp. 477–494, Dec. 2012, doi: 10.1007/s40065-012-0051-0.
W. M. Kozlowski, “On modulated topological vector spaces and applications,” Bull Aust Math Soc, vol. 101, no. 2, pp. 325–332, Apr. 2020, doi: 10.1017/S0004972719000716.
K. John L and Isaac Namioka, Linear Topological Vector Spaces. New York: Springer-Verlag, 1976.
J. Musielak, Orlicz Spaces and Modular Spaces. Berlin Heidelberg New York Tokyo: Springer-Verlag, 1983.
M. A. Krasnosel’skii and Y. B. Rutickii, “Convex Functions and Orlicz Spaces,” Groningen, 1961.
Haryadi and B. A. Nurnugroho, “Ruang Barisan Orlicz dan Ruang Dualnya,” Limits: Journal of Mathematics and Its Applications, vol. 19, no. 1, p. 123, May 2022, doi: 10.12962/limits.v19i1.8114.
