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Some results in metric modular spaces | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 81، دوره 13، شماره 2، مهر 2022، صفحه 983-988 اصل مقاله (370.09 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.25676.3091 | ||
| نویسندگان | ||
| Somaye Grailoo* 1؛ Abasalt Bodaghi2؛ Abolfazl Niazi Motlagh3 | ||
| 1Esfarayen University of Technology, Esfarayen, North Khorasan, Iran | ||
| 2Department of Mathematics, West Tehran Branch, Islamic Azad University, Tehran , Iran | ||
| 3Department of Mathematics, Faculty of Basic Science, Univercity of Bojnord, P. O. Box 1339, Bojnord, Iran | ||
| تاریخ دریافت: 03 دی 1400، تاریخ بازنگری: 15 اسفند 1400، تاریخ پذیرش: 22 اسفند 1400 | ||
| چکیده | ||
| A metric modular on a set $X$ is a function $w : (0,\infty)\times X\times X\longrightarrow [0,\infty]$ written as $(\lambda,x,y)\mapsto w_{\lambda}(x,y)$ satisfying, for all $x, y, z\in X$, the following three properties: $x = y$ if and only if $w_{\lambda}(x, y) = 0$ for all $\lambda>0$; $w_{\lambda}(x, y) = w_{\lambda}(y, x)$ for all $\lambda>0$; $w_{\lambda+\mu}(x, y) \leq w_{\lambda}(x, z) + w_{\mu}(y, z)$ for all $\lambda, \mu>0$. In this paper we define a Hausdorff topology on metric modular spaces and prove some known results of metric spaces including Baire's theorem and Uniform limit theorem for metric modular spaces. | ||
| کلیدواژه‌ها | ||
| modular؛ metric modular؛ Baire’s theorem؛ Uniform limit theorem | ||
| مراجع | ||
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