Certain Geometric Investigations of Three Normalized Bessel-Type Functions of a Complex Variable

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.

Authors

Rabab Alyusof (ORCID: https://orcid.org/0000-0002-5065-2774)
R. M. El-Ashwah (ORCID: https://orcid.org/0000-0002-5490-3745)
Shams Alyusof (ORCID: https://orcid.org/0000-0002-2787-9882)
Alaa H. El-Qadeem (ORCID: https://orcid.org/0000-0003-4478-4954)

Institutions

Damietta University (EG)
Zagazig University (EG)
Imam Mohammad ibn Saud Islamic University (SA)
King Saud University (SA)

Publication Details

Journal: Mathematics
Published: 2025-12-04
DOI: https://doi.org/10.3390/math13233888
Primary Topic: Analytic and geometric function theory
Type: article
Field-Weighted Citation Impact: 0.00

Funders

Al-Imam Muhammad Ibn Saud Islamic University

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article

Certain Geometric Investigations of Three Normalized Bessel-Type Functions of a Complex Variable

Rabab Alyusof, R. M. El-Ashwah, Shams Alyusof, Alaa H. El-Qadeem

Dec 4, 2025

Mathematics

Analytic and geometric function theory

article

Certain Geometric Investigations of Three Normalized Bessel-Type Functions of a Complex Variable

Rabab Alyusof, R. M. El-Ashwah, Shams Alyusof, Alaa H. El-Qadeem

December 4, 2025article en

Abstract

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.

MathematicsVol. 13(23)

Damietta University (EG), Zagazig University (EG), Imam Mohammad ibn Saud Islamic University (SA), King Saud University (SA)

Al-Imam Muhammad Ibn Saud Islamic University

Openalex Percentile: Top 57%

Analytic and geometric function theory

DOI Open Access PDF OpenAlex

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Certain Geometric Investigations of Three Normalized Bessel-Type Functions of a Complex Variable — Rabab Alyusof, R. M. El-Ashwah, et al. · Mathematics (2025) | TGRS Research Map | TGRS