Geometric Nature of the Turánian of Modified Bessel Function of the First Kind

This work explores the geometric properties of the Turanian of the modified Bessel function of the first kind (TMBF). Using the properties of the digamma function, we establish conditions under which the normalized TMBF satisfies starlikeness, convexity, <i>k</i>-starlikeness, <i>k...

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Bibliographic Details
Main Authors: Samanway Sarkar, Dimiter Prodanov, Anish Kumar, Sourav Das
Format: Article
Language:English
Published: MDPI AG 2024-12-01
Series:Axioms
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Online Access:https://www.mdpi.com/2075-1680/13/12/874
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Summary:This work explores the geometric properties of the Turanian of the modified Bessel function of the first kind (TMBF). Using the properties of the digamma function, we establish conditions under which the normalized TMBF satisfies starlikeness, convexity, <i>k</i>-starlikeness, <i>k</i>-uniform convexity, pre-starlikeness, lemniscate starlikeness, and convexity, and under which exponential starlikeness and convexity are obtained. By combining methods from complex analysis, inequalities, and functional analysis, the article advances the theory of Bessel functions and hypergeometric functions. The established results could be useful in approximation theory and bounding the behavior of functions.
ISSN:2075-1680