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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MDPI AG
2024-12-01
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| Online Access: | https://www.mdpi.com/2075-1680/13/12/874 |
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| author | Samanway Sarkar Dimiter Prodanov Anish Kumar Sourav Das |
| author_facet | Samanway Sarkar Dimiter Prodanov Anish Kumar Sourav Das |
| author_sort | Samanway Sarkar |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-bbb7e061394f40a484cf65c640502f01 |
| institution | DOAJ |
| issn | 2075-1680 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-bbb7e061394f40a484cf65c640502f012025-08-20T02:55:42ZengMDPI AGAxioms2075-16802024-12-01131287410.3390/axioms13120874Geometric Nature of the Turánian of Modified Bessel Function of the First KindSamanway Sarkar0Dimiter Prodanov1Anish Kumar2Sourav Das3Department of Mathematics, National Institute of Technology Jamshedpur, Jamshedpur 831014, IndiaLaboratory of Neurotechnology (PAML-LN), Institute for Information and Communication Technologies (IICT), Bulgarian Academy of Sciences, 1113 Sofia, BulgariaDepartment of Mathematics, Indian Institute of Technology Bhilai, Bhilai 492015, IndiaDepartment of Mathematics, National Institute of Technology Jamshedpur, Jamshedpur 831014, IndiaThis 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.https://www.mdpi.com/2075-1680/13/12/874analytic functionunivalent functionstarlike functionconvex functionBessel function |
| spellingShingle | Samanway Sarkar Dimiter Prodanov Anish Kumar Sourav Das Geometric Nature of the Turánian of Modified Bessel Function of the First Kind Axioms analytic function univalent function starlike function convex function Bessel function |
| title | Geometric Nature of the Turánian of Modified Bessel Function of the First Kind |
| title_full | Geometric Nature of the Turánian of Modified Bessel Function of the First Kind |
| title_fullStr | Geometric Nature of the Turánian of Modified Bessel Function of the First Kind |
| title_full_unstemmed | Geometric Nature of the Turánian of Modified Bessel Function of the First Kind |
| title_short | Geometric Nature of the Turánian of Modified Bessel Function of the First Kind |
| title_sort | geometric nature of the turanian of modified bessel function of the first kind |
| topic | analytic function univalent function starlike function convex function Bessel function |
| url | https://www.mdpi.com/2075-1680/13/12/874 |
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