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Baire's Theorem and Their Consequences in Modular Spaces | ||
| Journal of New Researches in Mathematics | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 10 دی 1401 | ||
| نوع مقاله: research paper | ||
| شناسه دیجیتال (DOI): 10.30495/jnrm.2022.65696.2213 | ||
| نویسندگان | ||
Mozhgan Talimian1؛ مهدی آژینی  2
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| 1Departmant of Mathematic ,Science and Research Branch ,Islamic Azad University, ,Tehran ,Iran | ||
| 2واحد علوم و تحقیقات، گروه ریاضی | ||
| چکیده | ||
| Many applications to di erential and integral equations with kernels of non power types were good reasons for the development of the theory of Orlicz spaces. Recently a new interest in classical Orlicz spaces is emerging in connection with problems of convexity, the Boyd indices and rearrangement invariant function spaces (see [8]). The succesful theory of Orlicz spaces inspired Nakano [11], to develop the theory of modular spaces in connection with the theory of order spaces. This was rede ned and generalized by Orlicz and Musielak. To control the pathological behavior of modular in modular spaces, some conditions such as 42..condition and the Fatou property are usually assumed (see, e.g., [1, 3, 5, 6, 10, 12]). For instance, in [1], Banach's xed point theorem is given in modular spaces that their modular satisfy both the 42..condition and the Fatou property. In this paper, we present and discuss some topological properties of modular spaces. Namely, we aim to prove the Baire's theorem and then open mapping and closed graph theorem in such spaces. | ||
| کلیدواژه‌ها | ||
| Modular spaces, Baire'؛ s theorem, Open mapping theorem, Closed graph theorem | ||
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آمار تعداد مشاهده مقاله: 11 |
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