Gyronormed Function Spaces | ||
| Mathematics Interdisciplinary Research | ||
| دوره 10، شماره 3، آذر 2025، صفحه 337-363 اصل مقاله (676.76 K) | ||
| نوع مقاله: Original Scientific Paper | ||
| شناسه دیجیتال (DOI): 10.22052/mir.2025.256568.1519 | ||
| نویسنده | ||
| Lorenzo Matarazzo* | ||
| Department of Engineering, Università degli Studi del Sannio, Campania, Italia | ||
| چکیده | ||
| In this paper, we introduce a gyrodistance on the gyrolinear space of functions (whose gyronorm is measurable) from a measure space to the Möbius disk $\mathbb{D}$. The gyrodistance in question can be expressed in terms of a modification of the Lebesgue integral, which we will call the Lebesgue gyrointegral. The gyronormed space generated in this manner, which we will call the $L^1$ gyrospace, is similar to the familiar $L^1$ function space in many aspects. We establish several properties of the latter, showing that many of them mirror those of classical $L^1$ spaces. Finally, we show that the gyrodistance in question induces a metric topology on the $L^1$ gyrospace. | ||
| کلیدواژهها | ||
| Gyrovector spaces؛ Gyrogroups؛ Gyrolinear spaces؛ Function gyrovector spaces | ||
| مراجع | ||
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