Analysis reveals that normalized Bessel-type functions exhibit convexity under defined bounds, indicating geometric significance in complex variables.
We recall the normalized forms for the three Bessel-type functions; these functions are the Bessel function, Lommel function, and Struve function of the first kind. By using convolution, we define normalized forms. The essential purpose is to introduce necessary and sufficient bounds of these normalized functions so these functions are starlike and convex of order γ and type δ.
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Alyusof et al. (2025) studied this question.
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