In this article, we derived conditions on the order $ \nu $ of the classical Bessel functions $ J_{\nu} $ that guarantee the inclusion of three distinct normalized forms of $ J_{\nu} $ in a subclass of $ \alpha $-spirallike functions. The primary goal was to determine the subintervals within $ (-\frac{\pi}{2}, \frac{\pi}{2}) $ where these inclusion conditions are satisfied. A key component in establishing our results was the upper bound of the ratio $ J_{\nu+1}(1)/J_{\nu}(1) $. The theoretical findings were validated through numerical experiments and accompanying graphical demonstrations.
Citation: Saiful Rahman Mondal, Ahlam Almulhim. Inclusion of Bessel functions in a subclass of spiral functions[J]. AIMS Mathematics, 2025, 10(8): 17362-17380. doi: 10.3934/math.2025776
In this article, we derived conditions on the order $ \nu $ of the classical Bessel functions $ J_{\nu} $ that guarantee the inclusion of three distinct normalized forms of $ J_{\nu} $ in a subclass of $ \alpha $-spirallike functions. The primary goal was to determine the subintervals within $ (-\frac{\pi}{2}, \frac{\pi}{2}) $ where these inclusion conditions are satisfied. A key component in establishing our results was the upper bound of the ratio $ J_{\nu+1}(1)/J_{\nu}(1) $. The theoretical findings were validated through numerical experiments and accompanying graphical demonstrations.
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Saiful Rahman Mondal, Ahlam Almulhim. Inclusion of Bessel functions in a subclass of spiral functions[J]. AIMS Mathematics, 2025, 10(8): 17362-17380. doi: 10.3934/math.2025776
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